Question

If $p\to (\sim p\vee \sim q)$ is false, then the truth values of p and q are respectively.

• A. T, F
• B. F, F
• C. F, T
• D. T, T

Answer 1

The correct option is D T, T

$p$	$q$	$\sim p$	$\sim q$	$\sim p\vee \sim q$	$p\to (\sim p\vee \sim q)$
T	T	F	F	F	F
T	F	F	T	T	T
F	T	T	F	T	T
F	F	T	T	T	T

It can be seen from the truth table that $p\to (\sim p\vee \sim q)$ is false only when $p$ and $q$ both are true.

Hence, answer is option (D).