If I study Hard -- then I will pass == Satisfied with result :) If I study Hard -- then I don't pass == not satisfied with result :( If I don't study hard -- then I pass == F**k Yeah I am satisfied :D I I don't study hard -- then I don't pass == F**k it, I didn't study so I am satisfied with results :) I hope this made better sense, these KZitem videos makes it more complicated sometimes :D
@sulemanahmed6770
4 жыл бұрын
you are a fucking legend. You helped me so much i was strugling to remember the if then table now i will not forget it. Thanks my g
@naff9n435
3 жыл бұрын
i knew something like this was similiar to domain and range fungtion. except the x variable where change to Truth varioable.
@lohitharudra7502
3 жыл бұрын
Helpful🔥
@leungwallace8552
3 жыл бұрын
Seems like not studying makes us satisfied anyway
@susanlaime1318
3 жыл бұрын
Thanks, now I remember.
@jbonceu2457
2 жыл бұрын
My thought process for this have always been: -If I guessed RIGHT then answered RIGHT, it make sense(it is RIGHT) -If I guessed RIGHT then answered WRONG, it doesn't make sense (it is WRONG) -If I guessed WRONG then answered RIGHT, it still make sense (It is RIGHT) -If I guessed WRONG then answered WRONG, it still make sense (It is RIGHT) Basically if you guessed Right in the first place, there's no reason for you to answer wrong, otherwise it will make the whole statement wrong(doesn't make sense). But if you guessed wrong in the first place, you cannot assume your answer will be right or wrong. So either way, any kind of conclusion will make the statement right (make sense)
@fallenangelonline3930
Жыл бұрын
omg this is so helpful, i learn faster this wayyy
@ahmed_mahrouky
Жыл бұрын
wow , you are brilliant, thanks
@ycombinator765
Жыл бұрын
WOW, You are a genius. Thanks for this so much!
@h3nry_t122
Жыл бұрын
I thought if p and q as a promise I promise that: if p happens then q will happen too if p happens -> q happens : True (promise is upheld) if p happens -> NOT(q happens) : False (promise is broken) if NOT(p happens) -> q happens : True (promise is upheld) if NOT(p happens) -> NOT(q happens) : True (promise is upheld) example: I promise that: if you have a dog then it is blue have dog -> color is blue : True have dog -> color is not blue : False have cat -> color is blue : True (original promise about dogs being blue is still True) have cat -> color is red : True (cats being red doesn't affect my promise) just because you have a cat doesn't mean my promise is broken. cause my promise is about DOGS being blue. cats got nothing to do with it.
@youtubeessentials2996
Жыл бұрын
🥰😍
@Pgonz7821
4 жыл бұрын
Bless my professor literally rushed through this entire topic in two sentences, gotta hate summer classes
@marciahuell
2 жыл бұрын
Likewise it's been a challenge for me finite maths
@victordadagaming928
6 ай бұрын
😢gdgxsfcl❤ggd🎉hdmvl@@marciahuell
@victordadagaming928
6 ай бұрын
Hvzlr
@stormyheadley764
4 жыл бұрын
This was incredibly helpful. My textbook feels so incredibly over-saturated with unnecessary information and it was overwhelming. The simplicity here and your clear explanation saved my grade this week! Thank you so much!
@DrTrefor
4 жыл бұрын
Glad it was helpful!
@rachalvinson-steckley8523
Жыл бұрын
@@DrTrefor 9
@senpaixd1346
Жыл бұрын
My textbook is written by someone who just wanted to fill the book with words without going through the trouble of explaining things
@TecknoVicking
Жыл бұрын
What I found ungrateful, is that without the textbook, you wouldn't have come here in the first place to understand. Let's honor the textbook for being (sometimes) way too dense.
@ShamSham519
6 жыл бұрын
Dude this was so helpful- I'm a visual learner and this is just brilliantly done
@badwrong
3 жыл бұрын
No such thing as a "visual learner"...
@makeki7756
3 жыл бұрын
@@badwrong veritasium
@ShamSham519
3 жыл бұрын
@@badwrong you’re correct that the term “visual learner” isn’t actually a real learning “style”. That being said, I still found the visual format of this video helpful for my comprehension on this subject matter. Take care :)
@hongminh4963
2 жыл бұрын
@@badwrong If there's no such thing "visual learner," then define it in a new way such that it exists.
@levinashon22
Жыл бұрын
@@badwrong Not true 😅 Pun intended 😅
@trendingnow-i6l
5 жыл бұрын
This is mirrored, are you really left handed!!! Your Voice guides me
@yuriroiter2167
4 жыл бұрын
Thank you, I finally got it looking this and other your videos! I had to develop a bit more resonating with myself explanation though. Hope it will help somebody more as well. :) Say, my (actually yours from another video :)) implication is: If it is a dog, then it is a mammal. Then, my implication is considering a dog (being a mammal) only, not a cat or a table. I agree (It is true) that when it is not a dog (p = false), then it can be anything -- mammal or not mammal (q is true or false). Thus, my implication is TRUE in both cases when it is not a dog -- then everything is all right with my implication, and I AGREE that (not a dog) can be anything. But when it is a dog, then my implication is ONLY TRUE when it is a mammal -- because it is what I specifically imply! Otherwise, my implication is FALSE. I.e. when it is a dog, and it is not a mammal -- then and only then my implication FAILS. Only then my implication is WRONG. CONCLUSION: Implication is FALSE ONLY when it is WRONG! Let's create a new boolean result: WRONG! :))
@iuseyoutubealot
2 жыл бұрын
loved this explanation
@deadchannel9624
4 жыл бұрын
this vid has been given to me by the online teacher cuz the quarantine
@Its.ary1220
4 жыл бұрын
Is this considered a tautology
@Mark-sc4bu
3 жыл бұрын
'Vacuous truths' - brilliant! Truth tables were easy right up to the p(false) implies q (true) line, and this has really stumped me. Other videos just say 'memorise the outputs' and failed to explain WHY the outputs were the way they are for conditional statements - memorising was easy but this video really helped me understand the underlying logic - thank you!
@jenniferbohannon7014
10 ай бұрын
"if p, then q" example is "if it is a dog (p), then it is blue (q)." This is logically equivalent to "it is either NOT a dog (p) OR it is blue (q)". It kind of makes sense if I think of it like this...
@AmandaLaVlog
6 жыл бұрын
Using this to study for the LSAT. Thanks for the video, helps a lot!
@cheesegyoza
2 жыл бұрын
I am not going to understand.
@konrad4478
11 ай бұрын
So that means IF I don’t study hard THEN I will pass the test anyway?
@astrosky4624
2 ай бұрын
Actually it's the ~
@300PIVOTMASTER
3 жыл бұрын
Explaining it using the ~p V q logical equivalency really helped me to finally grasp implication. Thanks!
@Juan-yj2nn
2 жыл бұрын
How is that ~p V q has nothing to do with real life implication?
@wintutorials2282
11 ай бұрын
@@Juan-yj2nn yes it does its kinda hard to explain but p implies q means: First: if p is true, q must be true (p=true IMPLIES that q=true) Second: if p isn't true, p IMPLIES q is also true, no matter what q is. (Think about it: if p isnt true, it's still true that a case where p is true, q is also true) Now what is true in any case here, if p-->q is true? If we look at both rules we find that the statement is always true when q is true or when p is false This gives ~p v q Now is this a coincidence or re they logically the same in any way? Well.. using human language to describe logic is difficult because human language is vague. The words we use to describe logic (if p then q / p implies q / p AND q etc) are ways to emulate the meaning of logic to human language. If the logic is the same, it's the same, in real life, anywhere. It means the same, it is the same in any way same or form. The thing that's different is our emulation of the logic. The word AND, is the closest we'll get to the real "logical meaning". The best way to emulate in human language/think about p --> q in my opinion is like this: --> is a logical operator that evaluates the truth value of a **promise of a theory leading to a conclusion** , where p is the hypothesis and q is the conclusion. Might sound difficult but if to bring it a little closer to human language: think of it like a scientist that promises you that if p is true, then q is true. Whether his promise is held or not determines the truth value . So if p=true leads to q being true, he doesn't break the the promise. If p=true leads to q being false, he breaks his promise: his theory didnt lead to the right conclusion. If p=false (his theory doesnt work) his entire promise isn't broken. It's the PROMISE (and the promise and all the logic, in whatever way you interpret that, what represents the logic of -->). For the promise to hold, the hypothesis being true what makes the conclusion being true a necessity For the promise to hold, the conclusion being false is what makes the hypothesis being false a necessity This is the relation of --> In logic terms: For p--> q to be true: p being true, REQUIRES q to be true (it won't hold when q is false) q being false REQUIRES p to be false (it wont hold if p is true) Hmmm.. so the logic is based on 2 requirements for two situations and all other situations are true it seems. (Just like how the logic of AND is based on 1 requirement: p and q need to be true at the same time) The 2 requirements, things that need to be true at least are: p being false or q being true In other words: ~p v q
@heyytabi
Жыл бұрын
This is why i like literature more😭😭😭😭
@reljasegvic6981
3 жыл бұрын
Yeah, I can see that you understand better than my profesor (since she couldn't even comprehend my question, only thing she new is a table she learned without applying the definition on conditional), but still at 6:51 ... NO, those two frases absolutely don't mean the same thing, and that is because of the reason you metioned before in video. The difference is than second frase does cover all the cases, while second one doesn't. 2:32 you said that we can't say that they are false, but there is neither a reason to say they are true. They are equally as true as they are false! The definition of conditional must be wrong, and it is being teached in all schools. Conditional must be written as ~a V b and that is the only way. If you say that conditional means if "A than B" the table you are giving isn't right. That is what I told my teacher when I first saw this, and according to her I am not smart enough to understand what is happening... The fact that there are teachers who don't understan their subject is very disturbing if you ask me... Relevance logic is "non classical" logic that suggests that when the first premise is false, implication is something in between true and false, and if we take the definition of conditional from the school textbooks that is the only correct answer.
@kristianholtedk
4 жыл бұрын
Thank you for explaining the scenarios where the initial statement is false :)
@missamal4553
5 жыл бұрын
finally i got the explanation that i want, ur smart and the way u explan is very clear ...thanks a lot
@Salvation1984
4 жыл бұрын
I was so stumped when I read this in my textbook, I'm prepping for my upcoming math class and want to understand the concepts before class starts. This was VERY helpful! Subscribed!
@DrTrefor
4 жыл бұрын
Really glad it helped, good luck in your class:)
@aruns.g.2799
4 жыл бұрын
Hi Trefor, thanks for this video. Quite a few books that I referred to skip the last two cases completely or gloss over it without going into even a minimal depth. I see you dint skirt the last two cases and in fact your study/pass example put things in better context. I'm taking Logic as a subject in a course on Philosophy and can see where this trouble originates. It lies in the epistemology of different philosophies. The classical Western/Aristotelian ( multi valued logic addresses this gap ) version of truth is True/False , 0/1. However classical /ancient Indian philosophy has a layered or more nuanced version of truth. 7 versions, actually, ranging from True to False! Some of the indeterminate ones are - somehow ( or sometimes) true, somehow ( or sometimes ) untrue, Both true and false ( think Both sides claiming victory in a war!), Neither true nor false.....etc. This layered approach to truth is reality of life and where all confusions, conflicts, distrust, outrage arise. When life is black & white, this works perfectly, but breaks down when things are grey. In short, the real answer to the 2 cases when P is "F" should be "unknown".
@Hooghog
2 жыл бұрын
Another way to think about the truth table with the statement "If you study hard, then you will pass". There are 4 cases: 1) I studied hard and I passed 'You said if I studied hard, then I would pass, and I did! You were right!' the statement is correct [TT->T] 2) I studied hard and I didn't pass 'You said if I studied hard, then I would pass, and I didn't! You were wrong!' the statement is incorrect [TF->F] 3) I didn't study hard and I passed 'I passed! You didn't mention what would happen if I didn't study hard, so for me you're not wrong!' the statement is correct [FT->T] 4) I didn't study hard and I didn't pass 'I didn't pass. You didn't mention what would happen if I didn't study hard, so for me you're not wrong!' the statement is correct [FF->T]
@jbonceu2457
2 жыл бұрын
Yes alot of people fail to comprehend at first that it's a hypothesis arriving to a conclusion kind of thing. The first statement was just a "guess". If you guessed right, there's no reason to conclude wrong (other wise it doesn't make sense, it's false). And if you guessed wrong, it makes the situation vague, hence any kind of conclusion to that statement makes sense (right)
@irwansyah1979
9 ай бұрын
This is the GREAT one
@ivanbenitez567
2 жыл бұрын
I'm currently studying this for university entrance exam here in Mexico, so I came across this chanel. Your explanation is definitely easier than my textbook but I was still confused with some parts of the video so I will have to watch it as many times as needed to get it all. Thanks for the content.
@majorlookgaming6070
Жыл бұрын
Thank you for helping my college algebra course make more sense. You rule.
@DrTrefor
Жыл бұрын
Thank you so much, really appreciate that!
@jayhun
2 жыл бұрын
this is going to help my valorant career
@rainbowestarz
7 жыл бұрын
I’m teaching truth tables to my students and this video is great!
@joemoe1739
3 жыл бұрын
I thought you we're Marc Gasol. You look very similar with your beard with him..
@Rams4ajnsz
3 жыл бұрын
I'm just here because my girlfriend was teaching me this early and I want to take interest in the things she enjoy.. great video now let me go make her happy
@satya8997
3 жыл бұрын
p disjunction q similar nagation nagation p conjunction nagation q truth table. Sir please solve the question
@chrishamilton1728
4 жыл бұрын
I think you need to make it clear that the example given was inclusive, meaning that if you don't study hard it is still possible to pass. At first the example seems exclusive, meaning that if you don't study hard, you won't pass, in which case the third column would be false. This caused some confusion for me.
@adrianbaranowicz507
4 жыл бұрын
Couldn't agree more. I'm surprised people are praising this material despite it being somehow incomplete, hence very confusing.
@IMAD007VLR
4 жыл бұрын
It is clearly exclusive, you are just not able to comprehend it
@anshulpatil1285
4 жыл бұрын
Thank you So Much Sir 🙌. Your Video Helped me Understand the very thing I was having a doubt in. This one was Precise and Short 👍
@cancelcancel6613
3 жыл бұрын
It's fun to learn when Marc Gasol is the one teaching you
@maliksaifaminoden9785
3 жыл бұрын
Lol. I also noticed that
@borissimovic441
3 жыл бұрын
I have an Intuitive explanation. My statement is: “Whenever I wear a blue jacket then I wear black shoes”. So, in the first row, this statement is true. But in the third row, it is also true, because I didn't say, that I wear black shoes only when I wear a blue jacket but that when I wear a blue jacket I wear black shoes (my point is that black shoes are not a condition for anything, I can wear black shoes with whatever I want, but when I wear a blue jacket then I must wear black shoes, so “blue jacket” is a condition that implies black shoes, and not another way around. This means that I can wear a white jacket and black shoes but the statement:” Whenever I wear a blue jacket then I wear black shoes” doesn't have anything to do with this, it is still true that always when I wear a blue jacket than I must wear black shoes. So this implication is not true only when I do something contradictory to what I claim, for example, I say that: “Whenever I wear a blue jacket then I wear black shoes” and then instead I take some other shoes, for example, I wear a blue jacket but I take some red Nike ✔️. Similarly is for the 4th row. But 2nd the row is the only one that is in contradiction with my statement or claim.
@mehakverma4195
3 жыл бұрын
7:08 mins worth it :) Thank you so much, Dr. Trefor Bazett
@hanshengchen615
4 жыл бұрын
'If I study hard, I will pass' does NOT mean if I don't study hard, I won't pass, does it? You logic seemed a little bit fuzzy in the explaination part
@georgedegroot816
4 жыл бұрын
if and only if! both statements are true. right? Logical biconditional
@jaivangordon5966
3 жыл бұрын
8-8 Check
@clue64
6 жыл бұрын
Thank you so much, I couldn't interpret that the statement was based if p was True in all scenarios of the conditional statement.
@AnuragGuptainspired
7 ай бұрын
Somebody please explain for these two statements: p = The weather is sunny q = We will go trekking How can we explain the truth table for p-->q in this case?
@saityusufbulur3366
2 ай бұрын
p -> q: If the weather is sunny, we will go trekking. If the weather is sunny and you go trekking (p is true and q is true), you will have fulfilled the promise, that is, the statement will be true. If the weather is sunny but you don't go trekking (p is true but q is false), you break the promise, meaning the statement is false. If the weather is NOT sunny (p is false), the statement is true whether you don't go trekking (q is also false) or you go (q is true). This is because you didn't make any promises about what you would do when the weather is NOT SUNNY. The promise you made was about what you would do if the weather was SUNNY. Therefore, if the weather is NOT SUNNY, your promise has no binding. Think of it this way. Let's say the weather is not sunny and you didn't go trekking, a friend of yours asked, "You said you were going trekking, did you change your mind ?" What answer would you give him ? a. "Yes, I changed my mind." b. "No, I haven't changed my mind. I said I would go when the weather was sunny, but it wasn't sunny, so I didn't go." Your answer will definitely be b, and it will logically satisfy your friend.
@mathst6575
2 жыл бұрын
My logic says that they are more vacuously false than true, especially for F=>T=T (I can think about F=>F=F more or less logically, but not about F=>T=T). To me, this does not look like logic but as a purely volitional decision to accept it as true, while it is neither true nor false. And I can't move on until I get it.
@jbonceu2457
2 жыл бұрын
My thought process for this have always been a hypothesis arriving to a conclusion (p-->q) -If I guessed RIGHT then answered RIGHT, it make sense(it is RIGHT) -If I guessed RIGHT then answered WRONG, it doesn't make sense (it is WRONG) -If I guessed WRONG then answered RIGHT, it still make sense (It is RIGHT) -If I guessed WRONG then answered WRONG, it still make sense (It is RIGHT) Basically if you guessed Right in the first place, there's no reason for you to answer wrong, otherwise it will make the whole statement wrong(doesn't make sense). But if you guessed wrong in the first place, you cannot assume your answer will be right or wrong. So either way, any kind of conclusion will make the statement right (make sense)
@account1307
4 жыл бұрын
Either I dont study hard, or I will pass Suppose I study hard, then I dont dont study hard, therefore I will pass. Therefore if I study hard, I will pass. :D
@montronics8430
5 жыл бұрын
Sir this is so helpful... It really helped me.
@suewaynegrossett1042
6 жыл бұрын
Feels like I'm in a class room😅😅😅😅
@hem4992
3 жыл бұрын
thank you very much. I have finals this week
@mutlugundiler4458
6 жыл бұрын
The most intellectual and satisfactory explanation of foundation of this confusing topic. Take away for me is "If you want to understand the foundations of logic, go to a mathematician". Highly appreciated. Thanks. Yet, how can I translate this to a metal detection system operation logic "If metal is detected (P), then set out the alarm (Q)" "If metal then alarm" is TRUE meaning the system is working as designed, "If metal then no alarm" is FALSE meaning that the system is not operating correctly, "If not metal then no alarm" is also TRUE and the system is also working properly, but, "If no metal then alarm" case considered vacuously TRUE confuses me here. It's not true, it's a false alarm, the system is malfunctioning. In electronic design, this case should be assigned "DON'T CARE" value (stay put / remain in the last state). But in logic "don't care" is not truth value. What am I missing to comprehend here?
@scuzzjumper
5 жыл бұрын
Is it because "don't care" is basically Null and therefore not an equation? I'm just a dullard shooting from the hip...Is it vacuosly true because it is absolutley zero?
@mauro9180
2 жыл бұрын
It seems that if the original statement was revised to, "*If and only if* metal is detected (P), then set out the alarm (Q)", then the truth value for each case would be the same as before, but the previous flawed case would output FALSE, which is what makes sense in that context.
@solareclipsedudefinale9026
Жыл бұрын
Because from ur statement "if metal is detected, then set out the alarm", it doesn't say anything about what happens when no metal is detected; so if no metal is detected, the premise wasn't even true so we aren't even ready to consider whether the whole implication was true since we couldn't get the condition to be met in the first place. And when that happens, as the professor stated, we call it vacuously true.
@srijankumaryadav9648
5 жыл бұрын
Sir nice vedio and you are looking like Chris Hemsworth 😃
@nd685
4 жыл бұрын
You are indeed good looking, professor!
@factsbyaditya1308
3 жыл бұрын
thank you sir
@Airaldi
3 жыл бұрын
I think this will help the most: "If p then q" isnt the same as "If and only if p, then q". "If p then q", only means that when p is true, then q should aswell be true. But it can also happen that p was not the case, but q still be true. We havent discard that possibility, we have just said that, "if p happends to be true, then q is true aswell", but we havent said, "only if p is true, then and only then q can be true aswell".
@hashemalattas9009
3 жыл бұрын
Ohmagaaaa
@iuseyoutubealot
2 жыл бұрын
any idea why it's not called a vacuous lie haha
@zoha1266
3 жыл бұрын
this just made my day like i understand this easily so grateful to you for that
@MagnusTheUltramarine
2 жыл бұрын
If P = I study hard, and ~P = I don't study hard, then when ~P gets the value false, does it mean ~P = False = I do study hard (which is equal to P)??
@MagnusTheUltramarine
2 жыл бұрын
how is it possible that: Either It's false that I don't study hard (~p=false) or I it's false that I pass (q=false) = False? -> Either I study hard or I don't pass = False
@MagnusTheUltramarine
2 жыл бұрын
I think i got the answer. What makes false "Either I study hard or I don't pass = False" is that it's false that there is only one way of passing the test, which what the phrase says. Note: Or is actually: Either I study hard or I don't pass or i study hard and i dont pass. since the last part is false we are left with only either: i study hard and pass or I dont study hard and I dont pass BUT this is false because of the fact that I got a case where i dont study and I pass which is true, and i have a case where i dont study and i dont pass which is true also, both vacuously true. This is confirmed by the fact that it's an IF THEN statement and not IF AND ONLY IF which is what makes this statement in question false. Basically the rejection of this statement confirms that there is one condition which makes the outcome true every time that the condition happens, but reaffirms that just because you got Q it doesn't mean there is only one way of reaching it P -> Q , and that it's not P Q All of this flows from the fact that we are dealing with ~P V Q = Either I dont study or I pass, and from this statement, all the 4 statements in the Truth table
@luism5514
6 жыл бұрын
This makes 0 sense
@apatshe8188
4 жыл бұрын
The written examples are terrific to understanding the concept. But APPLYING it to mathematical concepts is so HARD to translate into "statements". How is this done effectively?
@spencerjames9417
5 жыл бұрын
How do you think about if q then p?
@jaredmartin8944
3 жыл бұрын
Hey Dr. Trefor, you are amazing! Thanks for sharing it.
@alinategh4920
9 күн бұрын
One example that I find helpful for understanding this: p: "It is raining." q: "The ground is wet." p -> q: "If it is raining, then the ground is wet." - If it is indeed raining (p = true), and if the gorund is indeed wet (q = true), then my argument (p -> q) is RIGHT (p -> q = TRUE). - If it is indeed raining (p = true), but the ground is NOT wet (q = false), then my argument (p -> q) is WRONG (p -> q = FALSE). This is because it contradicts the claim that rain causes the ground to be wet. - If it isn't raining (p = false), then regardless of the condition of the ground (if it's wet or not), my argument remains RIGHT (p -> q = TRUE). This is because if the condition (rain) doesn't occur, the statement can't be proven false. Since we can't prove the falsity of the statement, it remains true. I like to think of this as: "Innocent (true) until proven guilty (false)."
@k7y
4 жыл бұрын
P Q P->Q English(study example) 1 1 1 if I study hard, then I will pass Statement is True 1 0 0 if I study hard, then I will not pass Statement is False 0 1 1 if I don't study hard, then I will pass This statement should be False but why is it True? 0 0 1 if I don't study hard, then I will not pass Statement is True
@calebus9149
3 жыл бұрын
Thank you so much for this video Dr. Bazett!! I had been spinning my wheels on this Critical Thinking module for the past six hours when I came across this video. Super helpful!! You're definitely getting a sub from me!
@DrTrefor
3 жыл бұрын
You're very welcome!
@abloodygun
10 ай бұрын
Why and How?😢😢😢😢😢😢
@abloodygun
4 ай бұрын
Thank you Sir 😊
@saityusufbulur3366
2 ай бұрын
This is how I handle it. Expression p -> q is; - true under all circumstances where p is NOT true - true under all circumstances where q is true If we combine these two ideas, the expression p -> q is true when p is NOT true OR q is true, and we can write it like this: ~p v q Therefore, the expressions p -> q and ~p v q are logically equivalent.
@globtier
3 жыл бұрын
Really great , I was really confused before watching ur video. Now my concept is crystal clear. Love u dude.
@mrbale1815
Жыл бұрын
p q statement result T T It is raining and the ground is wet. T T F It is raining and the ground is not wet. F F T It is not raining and the ground is wet. T F F It is not raining and the ground is not wet. T
@Shadowfax2
8 ай бұрын
My way of understanding is this: The only way the promise p->q is broken is if p is true but q is false. So the negation of p->q is p^~q. But p^~q is true only when p is true and q is false. So p->q is false only when p is true and q is false which explains why the bottom two rows are true for p->q Also the negation of p^~q is ~pvq which is same as p->q as explained in the video
@metafizykawspoczesna6499
7 ай бұрын
The true nature of implication is not entailment but opposition: kzitem.info/news/bejne/1Kumq5iBiISXgaw (English subtitles available) The "False imply true" problem is solved once and for all!
@yamatanoorochi3149
11 ай бұрын
We are studying our neighbor's dog P: this dog can climb up walls we asserted that P is unsound and improbable (P = F) Q = T: the dog actually managed to climb up the walls, so the study's results matched our hypothesis (P -> Q = T) Q = F: the dog can't climb up the walls, we are not surprised at all as it checks out with our expectations (P) being unsound and improbable (F) so the results are within expectations (T)
@CalypsoSnail
15 күн бұрын
Thank goodness for this video, I nearly cried trying to do my geometry homework with no knowledge of what a conventional statement was because my geometry teacher didn't explain what those where to anyone in the class.
@BimlasKnittingYarn
6 жыл бұрын
Bro if u want well earning from u tube then make some easy animated video related math
@joshua2136
12 күн бұрын
Or is always an inclusive or in this case right? I found the last part to be the most confusing.... because you could not study and still pass right... so in that last or statement it could have been both.
@Kliamframe
6 жыл бұрын
Hmm.. Starting to make sense
@pingtao8437
Жыл бұрын
Thanks for your video! I also found it hard to understand until I made this hypothesis: If math works then 2 is an even number. (Math works, so it must be true) If math works then 2 is not an even number. (Math works, then you can't say 2 is not an even number, so it's false) If math doesn't work then 2 is an even number. (Math doesn't work, you can get any conclusion) If math doesn't work then 2 is not an even number. (Math doesn't work, you can get any conclusion)
@davidbielsa5188
2 жыл бұрын
The concept of vacuously true is wrong to me, i dont understand it. Suppose p=you dont study. Q=you fail the exam. And p->q: if you dont study, you fail the exam, which makes sense. Then !p->q should not be true: if i study->i fail the exam. For me, !p->q is neither true nor false, since no information is given about what happens if you do study. You could pass or fail the exam.
@gracevijay3480
4 жыл бұрын
Tysm! It helped me a lott! God bless you!
@giusepperesponte8077
Жыл бұрын
I am so confused as to how you filmed this. What’s going on? Are you filming from the other side of glass? It looks like that’s what must be happening but if that were the case, everything written would be backwards, right? I see all the post effects that come up like the grids and whatnot, I’m just not understanding anything else. The only explanation I can think of is that he learned to write backwards but that’s not a realistic explanation. This is bugging me. Edit: I had a realization while watching this which should’ve been obvious. I’m assuming when you filmed the video, the writing was originally backwards and you mirrored the entire video with a video editing software to make the writing face in the proper direction. You’re not actually left handed. I’ll just say, I hope this is the explanation because it’s all I can come up with 😂
@jorgeuribera
3 жыл бұрын
I still don't understand the third case, can someone add the logic to my idea please? Maybe I can get it this way... Let's suppose I have a computer program: If A is done: Then do B So: 1st case: If A is done then B is done = program working (t->t=t) 2nd case: If A is done then B is not done = program not working (t->f=f) 3rd case: If A is not done then B is done = (this is the part I don't understand, for me in this case the program is not working, so f->t=f, but the truth table says it should be f->t=t, which for me is telling me that B is going to be done without taking in account if A is done, so why would I write the conditional in first place if it is not going to evaluate it?) 4th case: If A is not done then B is not done = program working (f->f=t)
@Hi_Brien
3 жыл бұрын
So implication and equivalence are different even though in language we often equate them. I'm like "I'll pass if I study hard" which is like saying q->p, that's a false statement in many casea BUT that does not mean p->q, which is a true statement. If I study I could do well or I could fail, and if I don't study I can do well because say it's easy and who needs to study truth tables(jk) or I might fail because. Studying implies passing, but it doesn't guarantee it. What I want to know, is what logic paths can I take to make q: me passing a totality?
@ZettoChannel
4 жыл бұрын
If i don't study, does that mean i'l will pass? (P False, Q is true and therefore it's true)
@diya9707
2 жыл бұрын
I wasnt able to wrap my head around why the bottom two rows were interpreted as True until I saw this video, thank you
@icasticasticast
2 ай бұрын
im a programmer and i was getting really frustrated because this should be a walk in the park for me and I wasn't getting it but turns out It's just an issue of it not "translating" to a language i understand. Really helped when you explained it like hypothesis and conclusion because then I was able to figure out what it means and "translate" it
@ptree1694
4 жыл бұрын
You're videos are going to be my savior in my discrete mathematics class. My professor is extremely confusing when she's trying to explain pretty much everything. The textbook helped, but there were still some things I needed some clarification on and you explained them perfectly. Thank you so much for taking the time to make these videos.
@zaxzaxx4561
11 ай бұрын
....SO....Here's something I'm trying to figure out: Would the statement 'If p then not q' be a valid conditional statement if q is a list of all the things that would negate p if one, any or all of the things that were on the q list were true? Anyone?
@estant5129
Ай бұрын
You completely lost me in assigning "T" to both row 3 & 4. You need to explain this clearer.
@ablemicky9923
4 ай бұрын
I just love the comparison with the either or thing...need real life example to make sense out of it..I see no sense in P been false and Q been True and conclusion True...sincerely..
@averylane8944
3 жыл бұрын
Proposition: If your pet is a dog, then your pet is a male. Suppose my pet is a dog… ok now I can check the gender… it turns out my dog is male… the statement must be true Suppose my pet is a dog… ok now I can check the gender… it turns out my dog is female… I've proven the statement false Suppose my pet is a cat… ok I could check the gender but it doesn't really matter because the statement only applies to dogs so I wouldn't be proving anything even if my cat was female… without evidence to prove that the statement wrong, I must assume that it is true. Suppose my pet is a bird… same logic applies as if my pet was a cat… without evidence to prove that the statement wrong, I must assume that it is true.
@uridimmuvltozwta1466
4 жыл бұрын
why is it ~pvq? I would think it would be p^q since they both have to be true to have a true result. By saying that p is false you have made a contradiction to the statement, p has to be true for q to be true. I would think that C would apply here in that when P is false the outcome is false regardless of q. if I study hard, then I will pass. If you did not study hard yet pass then you contradicted studying hard. all the statement is saying study=pass by NOT studying the statement is false. I am just stuck on why that is not the case, how not studying is not considered a contradiction to studying.
@mandwaleadi775
4 ай бұрын
the biconditional ones had confused a lot. I thought of this example which made a lot of sense to me. If your friend can fly by himself in the sky then you can too. The truth value of it is true
@tonireyes844
7 жыл бұрын
Sir,, you are BRILLIANT, note please about the subtitle it's HORRIBLE you can do better by fixing this problem Edit: most of the videos have the same problem
@tonireyes844
7 жыл бұрын
I use English sir .. but I'm not a native speaker that's why I have some problems with it , anyway thank you SIR for infos
@marcelstaiger9100
Жыл бұрын
I still don't get the reason why we "just take the bottom two cases as true" just because... someone able to explain the reasoning behind it? :)
@padraiggluck2980
Жыл бұрын
Thank you, thank you, thank you! I have been struggling to justify p F and q T and how the implication is T. My text book doesn’t explain and I never heard the phrase ‘vacuously True’ before.⭐️
@DrTrefor
Жыл бұрын
Glad it was helpful!
@andy12829
3 ай бұрын
What you explained is based on Tautology, but the result how they arrived at such logic is still not clear to me
@jasonkennedyhernandez4652
3 жыл бұрын
You saved me so much time studying. Everything just clicked.
@teinili
3 жыл бұрын
I have watched this video before. And I tried to understand this soooo many times but it still hasn't clicked :D Maybe this time
@mataal8770
4 жыл бұрын
How bout the second column(propostion) Example the proposition If it is raining then I am not wet. We can not always assume that he/she will be wet if it is raining right? What if he or she is inside the house, shade, building, or anywhere that water cannot reach but it is still raining and she is not wet then can we say that the a proposition of T implies F can also be true true? Please enlighten me more.
@allenlab4824
6 ай бұрын
Hello I am from india this question is in my text book your teaching was easily understanding thank you
@Nishh.24s
Жыл бұрын
This is helpful.. now u r a part of my JEE journey ❤❤
@dianedavidson5283
Жыл бұрын
I could study hard and still not pass. I could not study hard and still pass (if, for example, the material is easy for me).
@markconley5730
Жыл бұрын
thanks for trying but still didn;t get it to get up and to comprehend '2'56" the next utube i tried helped immensely kzitem.info/news/bejne/1Z-ds6qGhKSLeYI
@AlemsegedDejene
Жыл бұрын
Let p&q be proposition with true value t &f respectively , Which statement is true value t ???? pls
@withlovestephaniedenise7024
2 жыл бұрын
True. If It is snowing False. It is 0 degrees Then: Is is snowing is not true. It can be 0 degrees and not snowing. Is this correct?
@danielcash1037
11 ай бұрын
I love a teacher who is enthusiastic and teaches at an understandable speed. Such a good combo. It's so common you only get one of the two.
@yokowasis
2 жыл бұрын
So, basically if the p is false, we don't give a fuck about the result. might as well put it as true.
@superspeedm
3 жыл бұрын
If p then q If sun set, then turn the light on : Sun set => light on ok Sun does not set => light off ok Sun set => light off XXX Sun does not set => light on (here is my problem, in table should be ok but i don't find it logical, i think that it should not be true or false)
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