Question

If $\mathrm{p}\to (\mathrm{p}\wedge ~\mathrm{q})$ is false. Then the truth values of $\mathrm{p}$ and $q$ are respectively

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

Answer 1

The correct option is D

T, T

Explanation for Correct Option :

$p\to (p\wedge ~q)$ is False

p	q	~q	(p ∧~ q)	p->(p ∧~ q)
T	T	F	F	F
T	F	T	T	T
F	T	F	F	T
F	F	T	F	T

The table shows that we get false only when $\mathrm{p}$ and $q$ will be $\mathrm{TT}$.

$\therefore p\to (p\wedge ~q)$ is false when $\mathrm{p}$ is true and $q$ is true.

Hence Option (4) is correct