Propositional Logic (Solved Problem 6)

Discrete Mathematics: Propositional Logic (Solved Problem 6)
Topics discussed:
1. Solution of GATE-2009 question based on propositional logic.

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

#DiscreteMathematicsByNeso #DiscreteMaths #PropositionalLogic

[KeshariPiyush]

Anyone who can't understand how let me explain!!! Different and easy method

Final result is P + 'Q = 'Q + P(COMMUTATIVE LAW) = Q -> P (EQUIVALENT)
Now we know what should be in the box "<-" so now put this reverse implies that "<-" in the box for all the four options and see which one results in P ˇ Q (P or Q).

Just apply it in reverse order

For option B) P <- 'Q = 'Q -> P = Q ˇ P = P ˇ Q (true)

NOTE: "<-" because originally in table it is given P [] Q but our result is Q -> P

[Simplifiedsurveying]

I used truth tables and well, they give the same result.
Steps:
1. I added columns for -P and -Q
2. Added the columns for the questions and also P v Q
2. to solve the cols for P [] Q you look for the equivalent truth values for the new expression comparing them with that in the question in the table.

[U-TechTV]

Please, make video on Natural Deduction, Hoare Logic, preconditional and post conditional logic proof.

[advaithkumar]

another ( possible easier ) way is to note that the binary operator only gives false when p = F and q = T and also note that the or operator is false for p= F and q = F which suggests that either b or c is the answer. Write down their truth tables.

[proggenius]

wow ...a very best method to solve it!

[ashikurrahman]

what kind of logic you implement the final check
??

[mojtabaahmed]

Couldn't we just say that the " p[] q"....is equevelant to " q ->p"....and then just use the first implication law?!


It would be very simple that way

[myunusedbrainchannel]

Why can't we write - P[]Q = pq + p~q + ~pq +~p~q.
Instead of P[]Q = pq + p~q +~p~q.

[sumanpal]

please answer WHY P+P'Q'=(P+P')(P+Q') ?