Check out my new course in Propositional Logic: trevtutor.com/p/master-discrete-mathematics-propositional-logic It comes with video lectures, text lectures, practice problems, solutions, and a practice final exam!
Thank you very much! I struggled with memorizing the truth tables for a year now (our math teacher had said there is no other way!) but as you explained the mathematical way to make them, it seems a child's play now! Thank you again!
This method makes this so much less complicated! Thank you so much, you are really providing a service and I wish more teachers were as great at explaining as you are. 😭
I have been searching a lot of Discrete Mathematics courses, yours is far better than the rest even it is from MIT! I don't see the point why people spend thousands of dollars sitting in classroom listening to boring stuff and still getting confused. You should be given a medal for what you have done, and you are really talented at teaching. I have introduced your lecture series in my math course forum, please keep making fantastic courses!
You are a LIFE SAVER!! I've been struggling to get where the T/F came from but my textbook wishes it knew how to explain this subject so clearly... instantly subscribed!!
Your handwriting is legendary, kind sir :) On the real, when you described the implication operator as a response to the question "when am I lying to you?" my brain melted. I've been trying to understand that logic for quite some time. I'm really glad I subscribed to your channel (and yes, I'm binge-watching your series). I want to use this as a stepping stone to axiomatic set theory and such. Videos like this make me happy, so thank you (I'm not a math major or student in general, just a curious soul). Turns out Tensor analysis is heavily based on the notion of a manifold, which requires vector spaces, which requires axiomatic set theory, which requires these foundational lectures. You're paving pot-holes in my logic I never knew existed, so kudos to you.
You did an awesome job explaining these truth tables. I was reading my discrete textbook and it made no sense at all. The textbook really did not even explain it. The textbook just said this is "T" and this is "F". Thank you!
It has been two months since i started university and i was confused and didn't have any idea why the result was true or false you explanation are unique and helped me alot and i understand everything now THANKS
Concerning the Conditional Connective, I like to think that the negation is not implied in a statement. He has said before that the negation is a connective that attaches to a positive statement. Therefore, the two entries in which p is false will result in a positive outcome.
Thank you so much for bringing up the "think of when I am lying to you" when understanding p-->q stuff, I was thinking of it more in a logical way which was why I got stuck on why F T becomes T (wearing sunscreen when it's not sunny) because whilst not reasonable, the original proposition did not explicitly state it cannot happen. Much appreciated
There is a small imprecision at 3:53: It says that the number of rows on a truth table is 2 to the number of statements, however, "P" and "ㄱP" are two different statements, so their truth table should have 2*2 rows, which is 4 rows, but as we see at 1:45, their truth table has 2 rows, which is 2 to the 1. Therefore, it's more precise to say that the number of rows in a truth table is equal to 2 to the number of LETTERS. In this example, since "P" and "ㄱP" share the same letter, there is only 1 letter, so their truth table has 2 to the 1 rows, which is 2 rows.
I need a series like this for analysis as well. 3blue1brown doesnt have one yet. It is excellent and actually covers everything we did and most importantly it has TOUGH question that force yout o fully understand the concept. Not like our uni examples which are easy as hell but in the exam you get bombarded with difficult proofs
I watched 3 videos on this topic before this one, and this is the first time I get an explanation why p->q is true if p is false. This is why I hated university.
Why are we learning Conjunction and Disjunction? Well in Programing you get if,else if,else statement In this statement when we use if we use && operator here it means the both condition must be true....therefore we learn Conjunction and there is another operator called or || we use this to identify at least one condition is true.....hence we learn Disjunction... Can you relate Programing with Discrete Mathematics right now?
Thank you Sir for teaching me.May you enter in a straight path which lead you to the real destination, this golden chance will never be found.Now it is your right over me to guide you.I am like your son.You can obviously know me below my name.
TrevTutor, Organic Chemistry tutor, Flammable Maths, Andrew Dotson, Zach Star, Numberphile, BriTheMathGuy, all great channels people. And ai qm sure theres more. For astrophysics check out Dr. Becky's channel.
Hi! Trev, about the sunscreen example, I’m not sure why it’s 1 when u say “if it’s not sunny, I will wear sunscreen” (the third row of the table). Thanks!
It's because you aren't breaking your promise. Your promise is that if it's sunny, you'll wear sunscreen. It doesn't say ANYTHING about a promise when it's NOT sunny, so any of that is all free for you to do whatever. You can wear sunscreen just for fun when it's not sunny and you still aren't breaking your promise. Hope that makes sense
Explain to me how one satisfies the compound proposition of wearing sunscreen when it is sunny in the case of not having any sunshine or sunscreen on. How does the compounded conditional statement become true when both of the constituent statements are false?
would the double false not be true for the and statement, because when they are both true its correct but if they are both false should it not also be correct ?
Hi I have a question. I don’t understand why (A subset B iff x€B implies x €A) isn’t true. Is the correct statement supposed to be (x€B implies x€A iff A subset B). Thanks
7:00 so I know that when it's sunny out you will wear sunscreen, but why is the sentence "If it's not sunny out, I will wear sunscreen", true? I have been searching for this answer across youtube and have only been told that because p as the antecedent is false and q is true, therefore p->q is "vacuously" true as there is nothing to prove otherwise. Is there a better or easier-to-grasp explanation for this as I still have no idea why you wear sunscreen when it's not sunny out.
Don't take it as sentence example , see it in the mathematical way The p->q is true ( 1) only if p≤q So if it's not sunny , i don't care if you wear sunscreen ,( i don't consider you lying "so its 1 " ) I only care if its sunny outside . Hope it's helped
if i have a premise, "The store is open every day except Sunday. Parking is free on Saturday and Sunday", and a conclusion, "Parking is free and the store is open on Saturday", how should i make its truth table? our homework's so hard to understaaaand! Thank you for answering in advance
TheTrevTutor So if the question P: he is coward. R: he is rich. The real question is here 1. He is either coward or he is poor. So what will be the answer?
Sorry. I misread the statements. I'm not sure if I would translate "he is not rich" as "he is poor", since being "not rich" doesn't entail that someone is poor. P v Q would be ideal where Q: he is poor. But your professor may accept P v ~R.
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Check out my new course in Propositional Logic: trevtutor.com/p/master-discrete-mathematics-propositional-logic
It comes with video lectures, text lectures, practice problems, solutions, and a practice final exam!
Didn't go to Uni for 4 months, watched your videos, passed discrete maths.
mood @njit
Mad respec
trying to do the exact same thing
Why not? What is wrong?
thx for the tip
these videos are about to single-handedly keep me from dropping this class
WHAT A GREAT TEACHER SERIOUSLY!! THANKS A LOT.
yeah
Thank you very much!
I struggled with memorizing the truth tables for a year now (our math teacher had said there is no other way!) but as you explained the mathematical way to make them, it seems a child's play now! Thank you again!
This method makes this so much less complicated! Thank you so much, you are really providing a service and I wish more teachers were as great at explaining as you are. 😭
I have been searching a lot of Discrete Mathematics courses, yours is far better than the rest even it is from MIT! I don't see the point why people spend thousands of dollars sitting in classroom listening to boring stuff and still getting confused. You should be given a medal for what you have done, and you are really talented at teaching. I have introduced your lecture series in my math course forum, please keep making fantastic courses!
What is your forum! I want to join
You are a LIFE SAVER!! I've been struggling to get where the T/F came from but my textbook wishes it knew how to explain this subject so clearly... instantly subscribed!!
Thank you so much! My professor’s first example of a truth table was like a four variables long. These videos really fill in the cracks 🤙
One of the best teachers I have ever come across in math. Your pedagogy is absolutely superlative. Thanks Trevor
You're really good at teaching.
This is very helpful for computer science's discrete math.
Thank's a lot;)
Your handwriting needs to be turned into a font
If it were a little bit neater, maybe!
hahahaha my thought exactly. i love the handwriting its good especially for a man.
So...after this whole font talk, how are the maths marks looking?
@@sandramukuka aAA
Your handwriting is legendary, kind sir :) On the real, when you described the implication operator as a response to the question "when am I lying to you?" my brain melted. I've been trying to understand that logic for quite some time. I'm really glad I subscribed to your channel (and yes, I'm binge-watching your series). I want to use this as a stepping stone to axiomatic set theory and such. Videos like this make me happy, so thank you (I'm not a math major or student in general, just a curious soul). Turns out Tensor analysis is heavily based on the notion of a manifold, which requires vector spaces, which requires axiomatic set theory, which requires these foundational lectures. You're paving pot-holes in my logic I never knew existed, so kudos to you.
For precalc I did Organic Chemiatry tutor and now for Diacrete math it's you. Both of you guys are fantastic.
Thank you, sir.
After reviewing your videos I managed to do my first homework problem!
7:00 is so nicely explained with that example :)
Thankyou so much TrevTutor , I never understood this since college until now that i am professor. You saved my teaching career
Love you man. We went over this in class but the professor confused the hell out of me giving weird examples
Same here. I swear that most college professors are horrible instructors and lack the ability to explain the subject properly.
You did an awesome job explaining these truth tables. I was reading my discrete textbook and it made no sense at all. The textbook really did not even explain it. The textbook just said this is "T" and this is "F". Thank you!
The mathematical way of explaining the propositions/operators made it easier for me to memorize what those symbols do. Thanks!
"Why mathematicians love sunscreen", by TheTrevTutor. That could be a bestseller lol
you make it so easy, saved me an hour of meaningless lecture. Thank youuuu!
your explanation of conditionals was very clear and concise. very easy to follow. thank you very much.
This is so great. My professor basically doesn't explain anything, so I will be following your videos closely.
Presented in a very easy to understand way. Thanks!
my professor in uoft recommended your channel for our pre-lecture prep, good work man
aaa just taking up discrete maths and I had no idea about truth tables so thank you for this video! definitely helped a lot dude
You explain very well, i wish all my university doctors explained that well, i would actually watch the classes lol
omg this helped me understand conditionals so much, my lecturer couldnt even explain it half as well
I'm glad that I found your channel. Thank you so much
7:00 that is incredible
It has been two months since i started university and i was confused and didn't have any idea why the result was true or false you explanation are unique and helped me alot and i understand everything now THANKS
Just discovered this amazing channel and i subscribed. Thanks for these videos.
Thanks sooo much for your explanations. They are soo simple and clear.
I love how you explain and write... Keep it up.
Concerning the Conditional Connective, I like to think that the negation is not implied in a statement. He has said before that the negation is a connective that attaches to a positive statement. Therefore, the two entries in which p is false will result in a positive outcome.
Thanks once again Trev. The conditional case may seem confusing indeed but the sunscreen example and the mathematical view helped a lot.
Im gonna post here today and get back to you after i pass my subject discrete math :) today is august 29 2021 :)
Thank you so much for bringing up the "think of when I am lying to you" when understanding p-->q stuff, I was thinking of it more in a logical way which was why I got stuck on why F T becomes T (wearing sunscreen when it's not sunny) because whilst not reasonable, the original proposition did not explicitly state it cannot happen.
Much appreciated
Beautiful explanation I would love to become a teacher like you one day ✌️✌️✌️✌️✌️✌️🙌🙌🙌🙌
Thank you for your discrete math playlist, sir!
These videos are so friggin' great
Awesome explanation understood the conditional operator which I didn't in my class :)
There is a small imprecision at 3:53: It says that the number of rows on a truth table is 2 to the number of statements, however, "P" and "ㄱP" are two different statements, so their truth table should have 2*2 rows, which is 4 rows, but as we see at 1:45, their truth table has 2 rows, which is 2 to the 1. Therefore, it's more precise to say that the number of rows in a truth table is equal to 2 to the number of LETTERS. In this example, since "P" and "ㄱP" share the same letter, there is only 1 letter, so their truth table has 2 to the 1 rows, which is 2 rows.
This helped me so much, took a burden off of me thank you so much
I need a series like this for analysis as well. 3blue1brown doesnt have one yet. It is excellent and actually covers everything we did and most importantly it has TOUGH question that force yout o fully understand the concept. Not like our uni examples which are easy as hell but in the exam you get bombarded with difficult proofs
Good teacher God bless you
you;re like thoth the god of wisdom and knowledge, thanks man you're such a great teacher i wish if you're my teacher in uni.
you are a great man... its really high-quality content bro.. all the respect
clarified with conditional statements.. thank you!
Thank you for this video, it helped a lot.
Great explanation of conditionals, thank you!
Just a tip, Conditiona is always true, only exception if the first term is T and the second term is F. So T - F = F, everything else is true.
you are a life saver
Thanks ...it's really helpful
Thank you ur a life saver
thank you so much! It's really helpful
I watched 3 videos on this topic before this one, and this is the first time I get an explanation why p->q is true if p is false.
This is why I hated university.
thanks for blessing me
bro why am i even paying for a degree when i just go teach myself everything on youtube anyways with the help of great teachers like yourself
For conditional it makes intuitive sense when you understand that if p is true q must be true as well.
Also, thank you for videos. Trying to get a head start in university and you are helping out.
Informative...... 👌👌👌
Oh wow i would never thought there's a way to calculate the basic logic function (not, and, or)
Why are we learning Conjunction and Disjunction?
Well in Programing you get if,else if,else statement
In this statement when we use if we use && operator here it means the both condition must be true....therefore we learn Conjunction
and there is another operator called or || we use this to identify at least one condition is true.....hence we learn Disjunction...
Can you relate Programing with Discrete Mathematics right now?
Bless u ,man ,thank you so much
Thank you for the video!! Can you also make a video on truth trees, please?
Thank you so much for this!
helpful video 💗👏👏👏
I learned more in 20 minutes (this video plus the one before) than I learned from my professor who taught this for three hours.
thank you so much !
Very clear! thanks a lot
u can download truth table generator TruthTable2 from iTunes Store if u want to check correctness of homework
Thank you Sir for teaching me.May you enter in a straight path which lead you to the real destination, this golden chance will never be found.Now it is your right over me to guide you.I am like your son.You can obviously know me below my name.
Thanx it is very helpful for me..
What if you had a question that said build a truth table for 1+1=2 V 2+3>4 ? What will be the truth table?
TrevTutor, Organic Chemistry tutor, Flammable Maths, Andrew Dotson, Zach Star, Numberphile, BriTheMathGuy, all great channels people. And ai qm sure theres more. For astrophysics check out Dr. Becky's channel.
Hi! Trev, about the sunscreen example, I’m not sure why it’s 1 when u say “if it’s not sunny, I will wear sunscreen” (the third row of the table). Thanks!
It's because you aren't breaking your promise. Your promise is that if it's sunny, you'll wear sunscreen. It doesn't say ANYTHING about a promise when it's NOT sunny, so any of that is all free for you to do whatever. You can wear sunscreen just for fun when it's not sunny and you still aren't breaking your promise. Hope that makes sense
Explain to me how one satisfies the compound proposition of wearing sunscreen when it is sunny in the case of not having any sunshine or sunscreen on. How does the compounded conditional statement become true when both of the constituent statements are false?
would the double false not be true for the and statement, because when they are both true its correct but if they are both false should it not also be correct ?
Thank you soo much, youre the best
Hi I have a question. I don’t understand why
(A subset B iff x€B implies x €A) isn’t true.
Is the correct statement supposed to be
(x€B implies x€A iff A subset B). Thanks
thank you
thanks my guy
Thank u
Oh! This is like Programming Short-Circuiting !
7:00 so I know that when it's sunny out you will wear sunscreen, but why is the sentence "If it's not sunny out, I will wear sunscreen", true?
I have been searching for this answer across youtube and have only been told that because p as the antecedent is false and q is true, therefore p->q is "vacuously" true as there is nothing to prove otherwise. Is there a better or easier-to-grasp explanation for this as I still have no idea why you wear sunscreen when it's not sunny out.
Don't take it as sentence example , see it in the mathematical way
The p->q is true ( 1) only if p≤q
So if it's not sunny , i don't care if you wear sunscreen ,( i don't consider you lying "so its 1 " )
I only care if its sunny outside
.
Hope it's helped
if i have a premise, "The store is open every day except Sunday. Parking is free on Saturday and Sunday", and a conclusion, "Parking is free and the store is open on Saturday", how should i make its truth table? our homework's so hard to understaaaand! Thank you for answering in advance
THANK YOU!
Thanks maaaaaaaaaaaaaaaaaaaaan 🙏🙏
Hello, I like your videos. i would like to know how do you make your videos?
*if i get good mark then ur the boss of the boss's 😂 but thank you, you helped a lot*
7:20 was so helpful. My teacher sucked at that.
So a biconditional is an xnor logic gate.
In the second example of the first slide, why is it false?
You made a mistake at the conjunction and disjunction part. With a conjunction, it is max(p,q) and with a disjunction it is min(p,q) I think
love it
hi. How about p¬q ? how can you solve this?
thank you.
is it easier if p->q = p' and q?
Very helpful...
what if a statement contains "either/or" will it be translated by or(v) or by X-OR?
Depends on your instructor. Typically it's assumed that it is disjunction (v) unless stated as 'either .. or ... but not both'.
TheTrevTutor
So if the question
P: he is coward.
R: he is rich.
The real question is here
1. He is either coward or he is poor.
So what will be the answer?
P v R. He can be both and it is still true.
TheTrevTutor
Is it not P v ~R as it is stated that he is poor in the statement? As negation means the opposite value.
Sorry. I misread the statements. I'm not sure if I would translate "he is not rich" as "he is poor", since being "not rich" doesn't entail that someone is poor.
P v Q would be ideal where Q: he is poor. But your professor may accept P v ~R.