Question

Let $p,q,r$ be three logical statements. Then $p\to (q\vee r)$ is equivalent to

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

Answer 1

The correct option is C $(p\to q)\vee (p\to r)$

We know, $a\to b\equiv \sim a\vee b$
$\therefore p\to (q\vee r)\equiv \sim p\vee (q\vee r)$
$\equiv (\sim p\vee q)\vee (\sim p\vee r)$
$\equiv (p\to q)\vee (p\to r)$