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  4. The negation of the statement (p ∧ q) → (∼ p ∨ r) is

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Q. The negation of the statement $(p \wedge q) \to (\sim p \vee r)$ is

Mathematical Reasoning

Solution:

$\sim [( p \wedge q) \to (\sim p \vee r) ] \equiv (p \wedge q) \vee [\sim (\sim p \vee r)]$
$\equiv (p \wedge q) \wedge (p \wedge \sim r)$