Let p,q, and r be any three logical statements. Which of the following is true? Options: A . &nbsp ∼ ( p ∧ ∼ q ) = ∼ p ∧ q B . &nbsp ∼ ( p ∨ ∼ q ) = ∼ p ∧ q C . &nbsp ∼ ( p ∧ ∼ q ) = ∼ p ∧ ∼ q D . &nbsp ∼ ( p ∧ ∼ q ) = p ∧ q

Let p,q, and r be any three logical statements. Which of the following is true

Question -

Let p,q, and r be any three logical statements. Which of the following is true?

Options:

A .

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

B .

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

C .

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

D .

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

Answer: Option B
:
B

Only option C is correct. It is a direct application of Demorgan's law.
$\sim (p \lor \sim q) =\sim p \land \sim (\sim q) =\sim p \land q$

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