Practice Negation in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The negation of a statement P, written \neg P, is the statement with the opposite truth value: true when P is false, and false when P is true.
Flipping true to false or false to true. 'It is NOT the case that...'
Example 1
easyWrite the negation of each statement and determine its truth value: (a) '5 > 3', (b) 'All cats are black.'
Example 2
mediumSimplify \neg(\neg p \lor q) using logical laws.
Example 3
easyWrite the negation of: (a) 'It is raining', (b) 'x \ge 5', (c) 'Every student passed.'
Example 4
mediumBuild the truth table for \neg p and verify that p \land \neg p is always false (contradiction) and p \lor \neg p is always true (tautology).