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Question
Using truth table prove that p ˅ (q ˄ r) ≡ (p ˅ q) ˄ (p ˅ r)
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Solution
| I | II | II | IV | V | VI | VII | VIII |
| p | q | r | q ∧ r | p ∨ q | p ∨ r | p ∨ (q ∧ 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 | T | F | F | F |
| F | F | T | F | F | T | F | F |
| F | F | F | F | F | F | F | F |
From column (VII) and (VIII), we get p ∨ (q ∧ r) ≡ ( p ∨ q) ∧ ( p ∨ r)
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