Question

The false statement in the following is

• A. $p \land (\sim p)$ is a contradiction
• B. $(p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow \mspace{6mu}\sim p)$ is a contradiction
• C. $\sim(\sim p) \Leftrightarrow p$ is a tautology
• D. $p \vee (\sim p)$ ⇔ is a tautology

Answer 1

Answer: (B)

$(p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow \mspace{6mu}\sim p)$ is a contradiction

Answer 2

$p \Rightarrow q$ is logically equivalent to $\sim q \Rightarrow \mspace{6mu}\sim p$

∴ $(p \Rightarrow q) \Leftrightarrow (\sim q \Rightarrow \mspace{6mu}\sim p)$ is a tautology but not a contradiction.