Negation Math Example 2

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Example 2

medium
Simplify ¬(¬p∨q)\neg(\neg p \lor q) using logical laws.

Solution

  1. 1
    Apply De Morgan's Law to the outer negation: ¬(¬p∨q)=¬(¬p)∧¬q\neg(\neg p \lor q) = \neg(\neg p) \land \neg q.
  2. 2
    Apply double negation: ¬(¬p)=p\neg(\neg p) = p.
  3. 3
    Result: p∧¬qp \land \neg q.

Answer

¬(¬p∨q)≡p∧¬q\neg(\neg p \lor q) \equiv p \land \neg q
De Morgan's Law states ¬(A∨B)≡¬A∧¬B\neg(A \lor B) \equiv \neg A \land \neg B. Combined with double negation elimination ¬¬p≡p\neg\neg p \equiv p, complex negations simplify step by step.

About Negation

The negation of a statement PP, written ¬P\neg P, is the statement with the opposite truth value: true when PP is false, and false when PP is true.

Learn more about Negation →

More Negation Examples

Example 1 easy

Write the negation of each statement and determine its truth value: (a) '[formula]', (b) 'All cats a

Example 3 easy

Write the negation of: (a) 'It is raining', (b) '[formula]', (c) 'Every student passed.'

Example 4 medium

Build the truth table for [formula] and verify that [formula] is always false (contradiction) and [f

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Related Concepts

Logical Statement