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Question
Prove that p → (¬q v r) ≡ ¬p v (¬q v r) using truth table
Solution
| p | q | r | ¬p | ¬q | ¬q v r | p → (¬q v r) | ¬p v (¬q v r) |
| T | T | T | F | F | T | T | T |
| T | T | F | F | F | F | F | F |
| T | F | T | F | T | T | T | T |
| T | F | F | F | T | T | T | T |
| F | T | T | T | F | T | T | T |
| F | T | F | T | F | F | T | T |
| F | F | T | T | T | T | T | T |
| F | F | F | T | T | T | T | T |
From the table, it is clear that the column of p → (¬q v r) and ¬p v (¬q v r) are identical.
∴ p → (¬q v r) ≡ ¬p v (¬q v r)
Hence proved.
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