Mathematical Reasoning

The following statement (p → q) → [(~p→q)→q] is:

  1. a tautology
  2. equivalent to ~p → q
  3. equivalent to p → ~q
  4. a fallacy

Answer

(p → q) → ((~p → q) → q)

= (p → q) → ((p ∨ q) → q)

= (p → q) → ((~p ∧ ~q) ∨ q)

= (p → q) → ((~p ∨ q) ∧ (~q ∨ q))

= (p → q) → (~p ∨ q)

= (p → q) → (p → q)

= T

The correct option is A.