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Question
Using truth table, prove the following logical equivalence:
(p ∧ q) → r ≡ p → (q → r)
Solution
| 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| p | q | r | p∧q | (p∧q)→r | q→r | p→(q→r) |
| T | T | T | T | T | T | T |
| T | T | F | T | F | F | F |
| T | F | T | F | T | T | T |
| T | F | F | F | T | T | T |
| F | T | T | F | T | T | T |
| F | T | F | F | T | F | T |
| F | F | T | F | T | T | T |
| F | F | F | F | T | T |
T |
The entries in columns 5 and 7 are identical.
∴ (p ∧ q) → r ≡ p → (q → r).
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