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Question
Check whether the statement p → (q → p) is a tautology or a contradiction without using the truth table
Solution
P → (q → p)
≡ P → (¬q v p) ......[∵ implication law]
≡ ¬p v (¬q v p) ......[∵ implication law]
≡ ¬p v (p v ¬q) .......[∵ Commutative law]
≡ (¬p V p) v (¬p v ¬q) ......[∵ Distribution law]
≡ T v ¬(p ∧ q) ≡ T ......[Tautology]
Hence p → (q → p) is a Tautology.
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