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BITSAT 2024 Shift 1 Paper

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Question : 71 of 130

Marks: +1, -0

The Boolean expression

\sim(p \lor q) \lor (\sim p \land q)

is equivalent to

$p$
$\sim q$
$q$
$\sim p$

Solution:

The Boolean expression

\sim(p \lor q) \lor (\sim p \land q)

is simplified as follows:

Start with the given expression:

\sim(p \lor q) \lor (\sim p \land q)

Apply De Morgan's Law:

(\sim p \land \sim q) \lor (\sim p \land q)

Use the Distributive Law:

\sim p \land (\sim q \lor q)

By the Complement Law, (

\sim q \lor q

) is a tautology

(t)

:

\sim p \land t

Finally, apply the Identity Law:

\sim p

Therefore, the expression simplifies to

\sim p

.

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