Propositional Logic (Solved Problem 5)

Discrete Mathematics: Propositional Logic (Solved Problem 5)
Topics discussed:
1. Solution of GATE-2005 question based on propositional logic.

Music:
Axol x Alex Skrindo - You [NCS Release]

#DiscreteMathematicsByNeso #DiscreteMaths #PropositionalLogic

[AmarKumar-ijzn]

Sir, if I will make A & B true (i.e. T) in the case of C.
Then, our answer will be option C also.

[subhradipsaha]

I have a question.
From your videos, I understood that this problem can be solved using three methods.
1. Solving the propositional logic using Laws.
2. Substituting truth values directly into the proposition.
3. Using Truth Table.

Now, when solving,
a) x equivalence y
The proposition is not a Tautology when solved using the first and third methods.
But when using the second method is used, it is a Tautology.

b) x implies y
When using the first and then third method, it is NOT a Tautology.
When using the second method, it is a Tautology.

Why is this?

[shristisingh]

Sir d may be also correct plz give full explanation

[DOCUMENTARYRECORDS]

Plz can u make a detailed video on low and high pass filter

[ritvikreddy]

So everyone here is in doubt so i will explain how only b is correct so it would help the others who will be watching the video in 2022
so first what does tautology mean ?? if all the truth values of a particular proposition is true only then it is a tautology in all the other cases it is false
so now let us take the 1st option
1)X=Y now consider the truth values of p, q and r to be T, T and F so X=T or T implies F so now X=F and Y=T implies F or T implies F so now Y=F
so X=Y=F since in tautology all the truth values of a compound statement should be true but here X and Y are both false so X=Y is not a tautology
2) Let us take the same values of p and q from above so F implies F is true and you can check with other values of p and q too in each condition the truth value will always be T so X implies Y is a tautology
3)Now let p, q and r be T, F and F so X=F and Y=T so Y implies X is F so since Y implies X is false it doesn't satisfy the condition of tautology so y implies x is not a tautology
4)Now consider the same values of p, q and r from above T, T and F so X=F and Y=F now according to option take negation of Y so after taking the negation of Y now Y=T so negation Y implies X is now F which same as option 3 does not satisfy the condition of tautology so negation y implies X is not a tautology

I hope you understood my explanation

[twilight]

Can we simplify Y to be (P or Q)->R?