GO Classes Weekly Quiz 5 | Propositional Logic | Question: 2

Answer 1

• A. $p \rightarrow q$ is not equal to $q \rightarrow p$ and hence not equivalent.
• B. $\neg(p \vee q) = \neg p \wedge \neg q$ (Using De-Morgans Law) and hence equivalent.
• C. $p \rightarrow q$ $=$ $\neg q \rightarrow \neg p$ (Contrapositive) and hence equivalent.
• D. none of the above. 

Therefore, the false expression is option A and hence the correct answer.

Answer 2

(A) : q → p is converse of p → q and they are not equal. So its a false statement.

[Truth table can help in proving this] 

       p→ q is false when p is True, q is false.

       q→ p is false when q is True, p is false.

       Thus they cannot be equivalent (or equal)

 

(B) : ~(p V q) = ~p ^ ~q (by De -morgan’s law). So its a correct statement.

 

(C) : p → q = ~q → ~p (by contrapositive property). So its a correct statement.

 

Thus, the correct answer to this question would be option (A)

Answer 3

Only option A is False.