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Question
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r).
Solution
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| p | q | r | q ∧ r | p ∨ (q ∧ r) | p ∨ q | p ∨ r | (p ∨ q) ∧ (p ∨ r) |
| T | T | T | T | T | T | T | T |
| T | T | F | F | T | T | T | T |
| T | F | T | F | T | T | T | T |
| T | F | F | F | T | T | T | T |
| F | T | T | T | T | T | T | T |
| F | T | F | F | F | T | F | F |
| F | F | T | F | F | F | T | F |
| F | F | F | F | F | F | F | F |
The entries in the columns 5 and 8 are identical.
∴ p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
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