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

May 27, 2026Mathematics

ScanSolve AI Answer

May 27, 2026

Here are the solutions to the questions:

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

Step 1: Apply De Morgan's Law. The negation of $(p \wedge \sim q)$ is $\sim (p \wedge \sim q)$ . According to De Morgan's Law, $\sim (A \wedge B) \equiv \sim A \vee \sim B$ . $\sim (p \wedge \sim q) \equiv \sim p \vee \sim (\sim q)$

Step 2: Simplify the double negation. The negation of a negation is the original statement, so $\sim (\sim q) \equiv q$ . $\sim p \vee q$ The negation of the compound statement

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1. The negation of the compound statement (p q) is Step 1: Apply De Morgan's Law.

Asked on May 27, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

ScanSolve AI AnswerAnswered on May 27, 2026

Here are the solutions to the questions: 1. The negation of the compound statement (p q) is Step 1: Apply De Morgan's Law. The negation of (p q) is (p q). According to De Morgan's Law, (A B) A B. (p q) p ( q) Step 2: Simplify the double negation. The negation of a negation is the original statement, so ( q) q. p q The negation of the compound statement