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Question
Examine whether the following statement (p ∧ q) ∨ (∼p ∨ ∼q) is a tautology or contradiction or neither of them.
Solution
(p ∧ q) ∨ (∼p ∨ ∼q)
| A | B | |||||
| p | q | ∼p | ∼q | p ∧ q | ∼p ∨ ∼q | A ∨ B |
| T | T | F | F | T | F | T |
| T | F | F | T | F | T | T |
| F | T | T | F | F | T | T |
| F | F | T | T | F | T | T |
From the last coloumn
(p ∧ q) ∨ (∼p ∨ ∼q) is a tautology
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