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Question
Determine whether the following statement pattern is a tautology, contradiction or contingency:
(p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q)
Solution
| p | q | ∼p | ∼q |
p ∧ q |
∼p ∧ q | p ∨ ∼q | ∼p ∧ ∼q | (I) ∨ (II) ∨ (III) ∨ (IV) |
| (I) | (II) | (III) | (IV) | |||||
| T | T | F | F | T | F | T | F | T |
| T | F | F | T | F | F | T | F | T |
| F | T | T | F | F | T | F | F | T |
| F | F | T | T | F | F | T | T | T |
All the entries in the last column of the above truth table are T.
∴ (p ∧ q) ∨ (∼p ∧ q) ∨ (p ∨ ∼q) ∨ (∼p ∧ ∼q) is a tautology.
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