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Question
Prove that the following statement pattern is a tautology : ( q → p ) v ( p → q )
Solution
| (1) | (2) | (3) | (4) | (5) |
| p | q | q → q | p → q | ( q → q ) v ( p → q ) |
| T | T | T | T | T |
| T | F | T | F | T |
| F | T | F | T | T |
| F | F | T | T | T |
The truth table contains only T in the last column.
Hence, the given statement is a tautology.
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