Question

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

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

Answer 1

The correct option is C

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

Contrapositive of $x\to y$ is $\sim y\to \sim x$
Also, the negation of $(\sim p\wedge q)$ is $(p\vee \sim q)$ and the negation of $(q\wedge \sim r)$ is $(\sim q\vee r)$
So, we have contrapositive of $(\sim p\wedge q)\to (q\wedge \sim r)\equiv (\sim q\vee r)\to (p\vee \sim q)$