Question

Let $p,q,r$ denote the arbitary statements then, the logical equivalance of the statement $p\Rightarrow (q\vee r)$ is

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

Answer 1

The correct option is B $(p\Rightarrow q)\vee (p\Rightarrow r)$

We know that, $x\Rightarrow y\equiv \sim x\vee y$
$\therefore p\Rightarrow (q\vee r)\equiv \sim p\vee (q\vee r)$
$\equiv (\sim p\vee q)\vee (\sim p\vee r)$
$\equiv (p\Rightarrow q)\vee (p\Rightarrow r)$