Question

The contrapositive of $p\to (\sim q\to \sim r)$ is equivalent to

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

Answer 1

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

The contrapositive of $p\to (\sim q\to \sim r)$ is
$\equiv \sim (\sim q\to \sim r)\to \sim p$
$\equiv \sim (q\vee \sim r)\to p\equiv (\sim q\wedge r)\to \sim p$