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Mathematical Reasoning

Question

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The statement p → (q → p) is equivalent to

p → (p → q)

p → (p ∨ q)

p → (p ∧ q)

p → (p ↔ q)

Solution

B.

p → (p ∨ q)

p → (q → p) = ~ p ∨ (q → p)
= ~ p ∨ (~ q ∨ p) since p ∨ ~ p is always true
= ~ p ∨ p ∨ q = p → (p ∨ q).

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