Question

For any three simple statement $p,q,r$, the statement $(p\wedge q)\vee (q\wedge r)$ is true, when

• A. $p$ and $r$ true and $q$ is false.
• B. $p$ and $r$ false and $q$ is true.
• C. $p,q,r$ all are false.
• D. $q$ and $r$ true and $p$ is false.

Answer 1

Answer: (D)

$q$ and $r$ true and $p$ is false.

We draw truth table here.

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

Given that the value of $(p\wedge q)\vee (q\wedge r)$ is true.

As per this condition and given options, this is true only when

$p$ is False and $q$ & $r$ are True.