Question

Let $p,q,r$ be three statements. Then $(p\to (q\to r\left)\right)⟹\left(\right(p\wedge q)\to r)$ is

• A. neither tautology nor fallacy
• B. tautology
• C. fallacy
• D. contradiction

Answer 1

The correct option is B tautology

$(p\to (q\to r\left)\right)\equiv \sim p\vee (q\to r)$
$\equiv \sim p\vee (\sim q\vee r)$
$\equiv \left[\right(\sim p)\vee (\sim q\left)\right]\vee r$
$\equiv \sim (p\wedge q)\vee r$
$\equiv (p\wedge q)\to r$
Hence, given statement is tautology.