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.
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😭
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.
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.
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.
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. ❤
ru-vid.com/video/%D0%B2%D0%B8%D0%B4%D0%B5%D0%BE-WznmNvo0fn8.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
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 ?
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.
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?
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.
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
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".
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
