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Question
Prove that the following pair of statement pattern is equivalent.
p ↔ q and (p → q) ∧ (q → p)
Solution
| 1 | 2 | 3 | 4 | 5 | 6 |
| p | q | p↔q | p→q | q→p | (p→q)∧(q→p) |
| T | T | T | T | T | T |
| T | F | F | F | T | F |
| F | T | F | T | F | F |
| F | F | T | T | T | T |
In the above table, entries in columns 3 and 6 are identical.
∴ Statement p ↔ q and (p → q) ∧ (q → p) are equivalent.
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