Mathematical ReasoningHard
Question
The statement p → (q → p) is equivalent to
Options
A.p → (p → q)
B.p → (p ∨ q)
C.p → (p ∧ q)
D.p → (p ↔ q)
Solution
p → (q → p) = ~ p ∨ (q → p)
= ~ p ∨ (~q ∨ p) since p ∨ ~ p is always true
= ~ p ∨ p ∨ q = p → (p ∨ q).
= ~ p ∨ (~q ∨ p) since p ∨ ~ p is always true
= ~ p ∨ p ∨ q = p → (p ∨ q).
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