Question

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

• A. $(\sim q\wedge r)\to \sim p$
• B. $(q\to r)\to \sim p$
• C. $(q\vee \sim r)\to \sim p$
• D. none of these.

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
$\equiv \sim (\sim q\to \sim r)\to \sim p$
$\equiv \sim (q\vee \sim r)\to \sim p$
$\equiv (\sim q\wedge r)\to \sim p$