Question

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

• A. True
• B. False
• C. May be true or false
• D. Cannot conclude from given the information

Answer 1

The correct option is A

True

$p\Rightarrow q$ is false only when $p$ is true and $q$ is false.
Given that $(p\wedge \sim r)\Rightarrow (q\wedge r)$ is false.
Hence, $p\wedge \sim r$ is true and $q\wedge r$ is false.

Given that $q$ and $r$ are both false. Hence, $q\wedge r$ is false.
Since $r$ is false, $\sim r$ is true.
$p\wedge \sim r$ must be true. Hence, $p$ must be true.