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Question
Using the truth table verify that p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r).
Sum
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Solution
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
We have three variables: p, q, r
So total rows = 23 = 8
| p | q | r | q ∧ r | p ∨ (q ∧ r) | p ∨ q | p ∨ r |
| T | T | T | T | T | T | T |
| T | T | F | F | T | T | T |
| T | F | T | F | T | T | T |
| T | F | F | F | T | T | T |
| F | T | T | T | T | T | T |
| F | T | F | F | F | T | F |
| F | F | T | F | F | F | T |
| F | F | F | F | F | F | F |
p ∨ (q ∧ r) ≡ (p ∨ q) ∧ (p ∨ r)
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