Question

If p and q are simple statements, $p\iff \sim q$ is true when

• A. p is true and q is true
• B. Both p and q are false
• C. p is false and q is true
• D. none of these

Answer 1

The correct option is C

p is false and q is true

$p\iff q$ is true only when both $p$ and $q$ are true or both $p$ and $q$ are false.
Hence, $p\iff \sim q$ is true only when p is true and $\sim q$ is true or p is false and $\sim q$ is false.
$\Rightarrow p$ is false and $q$ is true or $p$ is true and $q$ is false.