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Question
Prove p → (q → r) ≡ (p ∧ q) → r without using the truth table
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Solution
P → (q → r)
≡ P → (¬q v r) ......[∵ implication law]
≡ ¬p v (¬q v r) .......[∵ implication law]
≡ (¬p v ¬q) v r ......[∵ Associative law]
≡ ¬(p ∧ p) v r ......[∵ DeMorgan’s law]
≡ (p ∧ q) → r ≡ T ......[∵ implication law]
Hence Proved.
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