QJEEM22Mac598: JEE Main 2022 Mathematics - Class 11 JEEM22Mac598 Solution: Let r {p, q, p, q} be such that the logical statement r ( p) (p …

Question

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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 :

Accepted Answer

Clearly r must be equal to $\sim$ p

$\because$ $\sim$ p $\vee$ $\sim$ p = $\sim$ p

and (p $\wedge$ q) $\vee$ $\sim$ p = p

$\therefore$ $\sim$ p $\Rightarrow$ p = tautology.

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