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Question
Using the truth table, verify
p → (p → q) ≡ ~ q → (p → q)
Solution
| 1 | 2 | 3 | 4 | 5 | 6 |
| p | q | ~q | p→q | p→(p→q) | ~q→(p→q) |
| T | T | F | T | T | T |
| T | F | T | F | F | F |
| F | T | F | T | T | T |
| F | F | T | T | T | T |
In the above truth table, entries in columns 5 and 6 are identical.
∴ p → (p → q) ≡ ~ q → (p → q)
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