Question

The following statement $(p\to q)\to \left[\right(\sim p\to q)\to q]$ is:

• A. a tautology
• B. equivalent to $\sim p\to q$
• C. equivalent to $p\to \sim q$
• D. a fallacy

Answer 1

The correct option is A a tautology

$(p\to q)\to \left[\right(\sim p\to q)\to q)]=(p\to q)\to ((p\vee q)\to q)=(p\to q)\to ((\sim p\wedge \sim q)\vee q)=(p\to q)\to ((\sim p\vee q)\wedge (\sim q\vee q))=(p\to q)\to (\sim p\vee q)=(p\to q)\to (p\to q)=T$