Question

Let $r\in \{p,q,\sim p,\sim q\}$ be such that the logical statement $r\vee (\sim p)\Rightarrow (p\wedge q)\vee r$ is a tautology. Then $r$ is equal to :

Answer 1

Sol. Clearly r must be equal to $\sim p$
$\because \sim p\vee \sim p=\sim p$
$\text{and}(p\wedge q)\vee \sim p=p$
$\therefore \sim p\Rightarrow p=\text{tautology.}$