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Question
Using the truth table, prove the following logical equivalence :
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
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Solution
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| A | B | ||||||
| p | q | p ↔ q | p ∧ q | ~p | ~q | ~p ∧ ~q | A V B |
|
T T F F |
T F T F |
T F F T |
T F F F |
F F T T |
F T F T |
F F F T |
T F F T |
By column number 3 and 8
p ↔ q ≡ (p ∧ q) ∨ (~p ∧ ~q)
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