Question

If $(p\wedge \sim r)\Rightarrow (q\vee r)$ is false and $q$ and $r$ are both false, then $p$ is

• A. true.
• B. false.
• C. may be true or false.
• D. data insufficient.

Answer 1

The correct option is A true.

We are given that $q$ and $r$ are both False,

so we construct a truth table using both the True and False values of $p.$

$p$	$q$	$r$	$\sim r$	$p\wedge \sim r$	$q\vee r$	$(p\wedge \sim r)⟶(q\vee r)$
T	F	F	T	T	F	F
F	F	F	T	F	F	T

We are given in the question that the value of $(p\wedge \sim r)⟶(q\vee r)$ is False, this is true when $p$ is true.