Question

If statement $(p\vee \sim r)\to (q\wedge r)$ is false and statement $q$ is true, then statement $p$ is

• A. true.
• B. false.
• C. may be true or false.
• D. None of these.

Answer 1

The correct option is C may be true or false.

$\because (p\vee \sim r)\to (q\wedge r)$ is false

$\Rightarrow (p\vee \sim r)$ is true, and $(q\wedge r)$ is false

Here $(q\wedge r)$ is false and $q$ is true (given)

$\Rightarrow$ $r$ is false

again $r$ is false and $(p\vee \sim r)$ is true

$\Rightarrow$ $p$ may be true or false.