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Question
Prove that the following statement pattern is equivalent:
(p v q) → r and (p → r) ∧ (q → r)
Sum
Solution
Truth table given is as follows :
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| p | q | r | A ≡ p v q | B ≡ p → r | C ≡ q → r | A → r | B ∧ C |
| T | T | T | T | T | T | T | T |
| T | T | F | T | F | F | F | F |
| T | F | T | T | T | T | T | T |
| T | F | F | T | F | T | F | F |
| F | T | T | T | T | T | T | T |
| F | T | F | T | T | F | F | F |
| F | F | T | F | T | T | T | T |
| F | F | F | F | T | T | T | T |
Thus from column 7 and 8 we get
∴ (p v q) → r = (p → r) ∧ (q → r)
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