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What is the negation of the compound statement (p q)?

Mathematics

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1. The negation of the compound statement (p∧∼q)(p \wedge \sim q) is

  1. Apply De Morgan's Law.

    The negation of (p∧∼q)(p \wedge \sim q) is ∼(p∧∼q)\sim (p \wedge \sim q). According to De Morgan's Law, ∼(A∧B)≡∼A∨∼B\sim (A \wedge B) \equiv \sim A \vee \sim B.

    ∼(p∧∼q)≡∼p∨∼(∼q)\sim (p \wedge \sim q) \equiv \sim p \vee \sim (\sim q)

  2. Simplify the double negation.

    The negation of a negation is the original statement, so ∼(∼q)≡q\sim (\sim q) \equiv q.

    ∼p∨q\sim p \vee q

    The negation of the compound statement

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