Question

If q is false and p $\land$ q$\leftrightarrow$r is true, then [2023] is a tautology.

• A. p$\lor$r
• B. (p$\land$r) $\rightarrow$ p$\lor$r
• C. (p$\lor$r) $\rightarrow$ p$\land$r
• D. p$\land$r

Answer 1

Answer: (B)

(p$\land$r) $\rightarrow$ p$\lor$r

Answer 2

Given $q$ is false, $p \land q$ is false so $r$ must be false for $p \land q \leftrightarrow r$ to be true. With $r =$ false, option (B) simplifies to $\text{false} \rightarrow p$, which is always true.