For any two statements p and q, the statement ∼ ( p ∨ q ) ∨ ( ∼ p ∧ q ) is equivalent to Options: A . &nbsp ∼ p B . &nbsp p C . &nbsp q D . &nbsp ∼ q

Answer: Option A : A ∼ ( p ∨ q ) ∨ ( ∼ p ∧ q ) = ( ∼ p ∧ ∼ q ) ∨ ( ∼ p ∧ q ) = ( ∼ p ∧ ( q ∨ ∼ q ) ) = ∼ p

For any two statements p and q, the statement ∼(p ∨ q)

Question -

For any two statements p and q, the statement $\sim (p \lor q) \lor (\sim p \land q)$ is equivalent to

Options:

A .

\sim p

B .

p

C . q

D .

\sim q

Answer: Option A
:
A

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

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