If you're referring to SDC, I am with you 100%. I mean, it wasn't all bad, but they really didn't explain themselves in some of the lessons. They barely touched on truth tables and logic gates, and the recurrence chapter was a complete mess.
Thank you for teaching in the simplest way possible. These concepts are deceptively difficult. It's easy to have false confidence in an incorrect conclusion.
You are making a rather dry material look exciting! I've given up on learning propositional logic quite a few times just because textbooks tend to teach it in a boring way. However, your style of teaching, your voice, intonations, and the coloured text agains black background are very lively and keep me awake and interested. Thank you. ❤
I was a bit confused about the difference between the ''if'' and ''only if'', so I read about it a bit. Let me write two statements "If there is an exam, then I procrastinate" vs "I procrastinate only if there is an exam". In the first one, exam implies procrastination. But, in the second one, there could be a case where there is an exam and I do not procrastinate, but if I do procrastinate then there is an exam. So, procrastination implies exam. So, only if changes the compound proposition to the converse of the if and vice versa. Hope this helps someone.
That did help me, so thanks! The logical leap is realizing that "I procrastinate only if there is an exam" hints at a case where you might not procrastinate if there is an exam. So if I do procrastinate then I can be certain that it was because of the exam. Only the exam can make me procrastinate. It's quite subtle. And if I say "I procrastinate if and only if there is an exam" then that becomes a bidirectional.
so p -> q is "if p, then q" which is also "p if only q" and "there is an exam only if i procrastinate" because if there is an exam it means i procrastinated? is that what that means? also i am currently cramming for an exam i procrastinated studying for so this example is triggering lol😭
I procrastinate only if there is an exam, but if you don’t procrastinate when there is exam, that means the statement is false? Please correct me if I’m wrong.
hello Prof. B, I got confused on #2 with the 'only if' (at 6:09 timestamp) -- I thought this was if and only if so, my answer was (p OR q) bidirectional r.
if anyone is confused by #2, remember there are three types of implications: converse, inverse, and contrapositive. "if and only if" is a biconditional but "only if" is a converse implication which is why they're switched.
Wouldn't 7:00 be r -> p (+) q ? Because: only if you choose ONE of them (one true), in which it can't be both true. In your example about disjunctions: exclusive Or, you gave an example: "Soup or Salad comes with an entree" so based off of this, it would be '(+)' not 'v'
I think in this case you can have both, because you pay for it. There is no rule that you can't buy both and receive a free sandwich for it, in contrast to the soup and salad entree example. In the soup or salad example you get it for free as an extra side dish. In other words, if you buy a sandwich or soup or both you can get a free sandwich, there is no rule for buying more than stated that will exclude you from getting the free sandwich. Hope it made sense im bad at explaining lol
In 10:06. I think we can say only younger than. We should define that You are 16 years old or younger. Or simply say: not older than 16. Because we have in s proposition "you are (older) than 16". Am I right ?
If it were "if and only if", then yes it would be. However, if it is "only if" as #2 in my example, it creates the reverse statement of if you used "if".
i guess not. they do mean two different things. "only if" just reverses the implication instead of making it a biconditional. "if and only if" makes it biconditional.
6:30 i have method for these type of questions ( only if questions ) because i dont know how do it , i get confused alot with it , so please correct me if i am wrong First i will rewrite the statement so i can use if and then instead of using - only if - , so it can be the conditional statement i know The new statment would be same as the one in the first question and i would solve it and i will get the same answer but heres the trick : at the end i know it would be ( p v q ) --> r just like the first one after i get this answer i would change the position of the variables so it can be : r --> ( p v q ) This is made up method by me 😂 and i tried to do it on two exercises and it worked , so please tell me if its a valid one so i can keep using it
Since we have already covered the converse of an implication, wondering why she didn't say #2 is the converse of #1. From #1 to #2, didn't the propositions on each side of -> change sides, which is how you get converse from the original implication.
For #2 at 6:30 shouldn't it be a biconditional? (If and only if.) You wrote it as: "If I get a free sandwich on Thursday, then I bought a sandwich or I bought soup." But that's the same thing as writing: "If (and only if) I buy a sandwich OR I buy a soup THEN I can get a free sandwich on Thursday." So it should be: (p v q) r or r (p v q)
"IF AND ONLY IF" doesn't have the same meaning as "ONLY IF". IF AND ONLY IF, is a biconditional statement, meaning that either both statements are true or both are false. So it is essentially and “IF” statement that works both ways. Note that IF AND ONLY IF is different than simply ONLY IF.
Hmm, maybe it's because I'm coming from everyday semantics but I don't think understand the difference between "if" and "only if". On question1, isn't "r" dependent on either "p" or "q" happening, just like on question 2? What difference does the word "only" make? Or is it that in discrete math it always means if we only have "if" the hypothesis implies the conclusion, if we have "only if", the conclusion implies the hypothesis, and if we have "if and only if" it's biconditional?
i struggled with this too but found this website very helpful in explaining it: www.khanacademy.org/test-prep/lsat/lsat-lessons/logic-toolbox-new/a/logic-toolbox--if-and-only-if
This is a helpful explanation you may want to look at: www.khanacademy.org/test-prep/lsat/lsat-lessons/logic-toolbox-new/a/logic-toolbox--if-and-only-if
Why is the first practice not an exclusive or? Cause I wont be able to go to the movies and the store at the same time. So both being true will be a false. Can someone explain?
Hello, 5:54 shouldn't (p or q) be an exclusive or? because it says you buy a sandwich or a cup of soup. so if we buy both aren't we entitled for 2 free sandwiches?
I might not be entirely correct when I say this, but if the sentence were " Either a cup of soup or a sandwich gets you a free sandwich on Thursday" the exclusive or would have been used. When you say "either this or that, you assume just one to be true but not both. Here, the way the sentence is, the hypothesis of buying a cup of soup or a sandwich both grant you a free sandwich. This is much like "You get access to the library if you are a student or have a library card". So, if you are a student but also have a library card, you still get to access the library. And yes since there is no implication of only accepting one of the choices, you could get two free sandwiches if you buy both. Please feel free to correct me if I am wrong. :)
For practice one, it seems that the solution wouldn't make sense in the real world. For example if (p v q) -> r were true as you defined, I could buy a soup or sandwich on Monday and expect to come back Thursday for my free sandwich. I feel like dividing the problem like so makes more sense. p:Buy soup or sandwich q:It is Thursday r: Get a free sandwich (p ^ q) -> r
wait what about when the variables are connected by an OR operator or an AND, like lets say its in the form -q || (-p && q). my p is the election is decided. p is the votes have been counted.
@@stephenhemingway9435 That is correct. A negation of "I am older than 16" would be "It is not the case that I am older than 16" so "I am 16 or younger"
English is my second language so I really apologize if I make a mistake. I think the negation of ' you are older than 16 years old ' that should be younger than or equal to 16 years old' at 10:16 in the video
Be careful not to use “q only if p” to express p → q because this is incorrect. According to Kenneth H. Rosen in Discrete Mathematics and Its Applications.
I have to say, this is much more understandable than other courses around discrete math I saw so far, thank you for doing it!
If you're referring to SDC, I am with you 100%. I mean, it wasn't all bad, but they really didn't explain themselves in some of the lessons. They barely touched on truth tables and logic gates, and the recurrence chapter was a complete mess.
Thank you for teaching in the simplest way possible. These concepts are deceptively difficult. It's easy to have false confidence in an incorrect conclusion.
You are making a rather dry material look exciting! I've given up on learning propositional logic quite a few times just because textbooks tend to teach it in a boring way. However, your style of teaching, your voice, intonations, and the coloured text agains black background are very lively and keep me awake and interested. Thank you. ❤
Thanks so much!
I was a bit confused about the difference between the ''if'' and ''only if'', so I read about it a bit. Let me write two statements "If there is an exam, then I procrastinate" vs "I procrastinate only if there is an exam". In the first one, exam implies procrastination. But, in the second one, there could be a case where there is an exam and I do not procrastinate, but if I do procrastinate then there is an exam. So, procrastination implies exam. So, only if changes the compound proposition to the converse of the if and vice versa. Hope this helps someone.
That did help me, so thanks! The logical leap is realizing that "I procrastinate only if there is an exam" hints at a case where you might not procrastinate if there is an exam. So if I do procrastinate then I can be certain that it was because of the exam. Only the exam can make me procrastinate. It's quite subtle.
And if I say "I procrastinate if and only if there is an exam" then that becomes a bidirectional.
so p -> q is "if p, then q" which is also "p if only q" and "there is an exam only if i procrastinate" because if there is an exam it means i procrastinated? is that what that means?
also i am currently cramming for an exam i procrastinated studying for so this example is triggering lol😭
For me I do the example if it's only if as if and then and when I get the final answer I would change the position of the variables
I procrastinate only if there is an exam, but if you don’t procrastinate when there is exam, that means the statement is false?
Please correct me if I’m wrong.
your explanation is very clear, thank you for you hard work. I'm very appreciative of this playlist
so far this is helping me a lot, thank you professor.
hello Prof. B, I got confused on #2 with the 'only if' (at 6:09 timestamp) -- I thought this was if and only if so, my answer was (p OR q) bidirectional r.
apparently "only if" is not equivalent to "if and only if". For "only if" you converse the atomic propositions
@@emerald_eyes best way to put it thank you so much.
I'm just loving this series. I am really hopeful to improve my logical thinking with your lectures! Thank you Professor B!
if anyone is confused by #2, remember there are three types of implications: converse, inverse, and contrapositive. "if and only if" is a biconditional but "only if" is a converse implication which is why they're switched.
Thanks a lot, I got it confused with "if and only if".
Really glad i checked the comments.
Enjoyed the lesson! ❤ 😊
Splendid video as always. The 'only if' got me. :)
Me too! I think I messed it up in my first video and fixed it on the re-record
Thank you for all these lessons. I am complimenting these lessons with the actual text by Kennneth Rosen and it has been going great. Thanks again!
th-cam.com/video/WznmNvo0fn8/w-d-xo.html agar even questions chahiye to channel ko subscribe karain! aur comment mein apnay questions batai.
Wouldn't 7:00 be r -> p (+) q ? Because: only if you choose ONE of them (one true), in which it can't be both true. In your example about disjunctions: exclusive Or, you gave an example: "Soup or Salad comes with an entree" so based off of this, it would be '(+)' not 'v'
I think in this case you can have both, because you pay for it. There is no rule that you can't buy both and receive a free sandwich for it, in contrast to the soup and salad entree example. In the soup or salad example you get it for free as an extra side dish. In other words, if you buy a sandwich or soup or both you can get a free sandwich, there is no rule for buying more than stated that will exclude you from getting the free sandwich. Hope it made sense im bad at explaining lol
I'd rather choose it is OR, not XOR, too. Because there is no such statement that restricts us to buy both items.
Tqsm mam😊
professor as said there are a lot of ways to translate the sentence, so my question is how would I know I did right way?
I APPRECIATE FOR YOUR EXPLAIN
THANK YOU VERY MUCH
In 10:06.
I think we can say only younger than.
We should define that
You are 16 years old or younger.
Or simply say: not older than 16.
Because we have in s proposition "you are (older) than 16".
Am I right ?
AT 7:31, wouldn't it be biconditional for #2
If it were "if and only if", then yes it would be. However, if it is "only if" as #2 in my example, it creates the reverse statement of if you used "if".
@@SawFinMath Thank you for the explanation!
Is "only if" the same with "if and only if" statement?
i guess not. they do mean two different things. "only if" just reverses the implication instead of making it a biconditional. "if and only if" makes it biconditional.
I used p XOR q for number 2 after I rewrote it @6:48 Was I wrong?
you are better than Rutgers professors
I didn`t get the second part
Shuldn`t we use Biconditional for that!?
that's what I thought too. Discrete mathematics is hard! I hope I pass.
6:30 i have method for these type of questions ( only if questions ) because i dont know how do it , i get confused alot with it , so please correct me if i am wrong
First i will rewrite the statement so i can use if and then instead of using - only if - , so it can be the conditional statement i know
The new statment would be same as the one in the first question and i would solve it and i will get the same answer but heres the trick :
at the end i know it would be
( p v q ) --> r just like the first one
after i get this answer i would change the position of the variables so it can be :
r --> ( p v q )
This is made up method by me 😂 and i tried to do it on two exercises and it worked , so please tell me if its a valid one so i can keep using it
Since we have already covered the converse of an implication, wondering why she didn't say #2 is the converse of #1. From #1 to #2, didn't the propositions on each side of -> change sides, which is how you get converse from the original implication.
It is the converse of #1
For #2 at 6:30 shouldn't it be a biconditional? (If and only if.)
You wrote it as: "If I get a free sandwich on Thursday, then I bought a sandwich or I bought soup." But that's the same thing as writing:
"If (and only if) I buy a sandwich OR I buy a soup THEN I can get a free sandwich on Thursday."
So it should be:
(p v q) r
or
r (p v q)
"IF AND ONLY IF" doesn't have the same meaning as "ONLY IF".
IF AND ONLY IF, is a biconditional statement, meaning that either both statements are true or both are false. So it is essentially and “IF” statement that works both ways. Note that IF AND ONLY IF is different than simply ONLY IF.
@@Yuzema Thanks. Helped me a lot
In 1.1.2, the q statement was "I won't go to town". Is there a reason we left that as a negative but not here?
Hmm, maybe it's because I'm coming from everyday semantics but I don't think understand the difference between "if" and "only if".
On question1, isn't "r" dependent on either "p" or "q" happening, just like on question 2? What difference does the word "only" make?
Or is it that in discrete math it always means if we only have "if" the hypothesis implies the conclusion, if we have "only if", the conclusion implies the hypothesis, and if we have "if and only if" it's biconditional?
i struggled with this too but found this website very helpful in explaining it: www.khanacademy.org/test-prep/lsat/lsat-lessons/logic-toolbox-new/a/logic-toolbox--if-and-only-if
@@Buzzius88 Thank you so much
This is a helpful explanation you may want to look at: www.khanacademy.org/test-prep/lsat/lsat-lessons/logic-toolbox-new/a/logic-toolbox--if-and-only-if
Why is the first practice not an exclusive or? Cause I wont be able to go to the movies and the store at the same time. So both being true will be a false. Can someone explain?
Can I write question 2 as (p ^ Q) --> r
Hello, 5:54 shouldn't (p or q) be an exclusive or? because it says you buy a sandwich or a cup of soup. so if we buy both aren't we entitled for 2 free sandwiches?
Can anyone please answer this question?
I might not be entirely correct when I say this, but if the sentence were " Either a cup of soup or a sandwich gets you a free sandwich on Thursday" the exclusive or would have been used. When you say "either this or that, you assume just one to be true but not both.
Here, the way the sentence is, the hypothesis of buying a cup of soup or a sandwich both grant you a free sandwich. This is much like "You get access to the library if you are a student or have a library card". So, if you are a student but also have a library card, you still get to access the library.
And yes since there is no implication of only accepting one of the choices, you could get two free sandwiches if you buy both.
Please feel free to correct me if I am wrong. :)
Can you make a video on the Growth of Functions section? I'm having a hard time on this section. I'd really appreciate it. Thank you.
Sorry! I didn't see this, and also I'm working now on Calc II and then Abstract. Once I'm done with those courses I'll have more time on my hands.
you ma heart fr
I'm not a native english so it feels like 2 in 1 course for me
For practice one, it seems that the solution wouldn't make sense in the real world. For example if (p v q) -> r were true as you defined, I could buy a soup or sandwich on Monday and expect to come back Thursday for my free sandwich. I feel like dividing the problem like so makes more sense.
p:Buy soup or sandwich
q:It is Thursday
r: Get a free sandwich
(p ^ q) -> r
wait what about when the variables are connected by an OR operator or an AND, like lets say its in the form -q || (-p && q). my p is the election is decided. p is the votes have been counted.
Thanks
If I am not older than 16, am I not
Meaning
@@stephenhemingway9435 That is correct. A negation of "I am older than 16" would be "It is not the case that I am older than 16" so "I am 16 or younger"
This is extra hard when your first language is not english.
9:20 The white looks like pseudo code in programming
English is my second language so I really apologize if I make a mistake. I think the negation of ' you are older than 16 years old ' that should be younger than or equal to 16 years old' at 10:16 in the video
Be careful not to use “q only if p” to express p → q because this is incorrect. According to Kenneth H. Rosen in Discrete Mathematics and Its Applications.
I disagree."Only If" is one-directional and in the opposite order of what is stated.
70
You should you exclusive or for the sandwich or a cup of soup?