Discrete Math 1.2.1 - Translating Propositional Logic Statements

Translate from English to propositional statements and back again.

Video Chapters:
Introduction 0:00
Translate English Into Propositional Logic 0:06
Practice 3:06
Translating Propositions into English 8:20
Up Next 11:05

Textbook: Rosen, Discrete Mathematics and Its Applications, 7e

[HolyShadowNow]

I have to say, this is much more understandable than other courses around discrete math I saw so far, thank you for doing it!

[pen]

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.

[InSterquiliniisInvenitur]

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.

[LaraPierre-nb]

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.

[chessketeer]

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. ❤

[angelcp]

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.

[ulysses_grant]

I'm just loving this series. I am really hopeful to improve my logical thinking with your lectures! Thank you Professor B!

[MustafaAli-dduz]

so far this is helping me a lot, thank you professor.

[jasperling]

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'

[fauxhawkboy]

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!

[aliredha]

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 ?

[raccon]

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?

[samriego]

Is "only if" the same with "if and only if" statement?

[saroopmakhija]

you are better than Rutgers professors

[annoyingprecision]

Splendid video as always. The 'only if' got me. :)

[TheMountainBeyondTheWoods]

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?

[HeisenbergHK]

I didn`t get the second part
Shuldn`t we use Biconditional for that!?

[Salamanca-joro]

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

[taekwondotime]

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)

[utbin]

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.