Question

$(p\wedge q\leftrightarrow r)$ is true and $q$ is false then which one of the following is a tautology?

• A. $(q\vee r)\to (p\wedge r)$
• B. $p\vee r$
• C. $p\wedge r$
• D. $(p\vee r)\to (p\wedge r)$

Answer 1

The correct option is A $(q\vee r)\to (p\wedge r)$

Given $q$ is $F$ and $(p\wedge q)\leftrightarrow r$ is $T$

$⟹p\wedge q$ is $F$ which implies that $r$ is $F$
$⟹q$ is $F$ and $r$ is $F$

$⟹(q\vee r)$ is always $F$

$⟹(q\vee r)\to (p\wedge r)$ is tautology.