Part IV: Constructing proofs of equivalence (25 pt.) To prove that a biconditional statement of the form pq is true, we must show that p q and q p are both true. The validity of this approach is based on the tautology: For example, to prove that for any integer n, n is odd if and only if n2 is odd, we must show that (1) if n is odd, then n2 is odd, and (2) if n2 is odd, then n is odd. 1. (10 pt.) Prove that for any positive integer n, n is even if and only if 5n 6 is even. Indicate which proof methods you used, as well as the assumptions (what you suppose) and the conclusions (what you must show) of the proof Sometimes a theorem states that several propositions pi, p2,., and pn are equivalent. To prove that a statement of this form is true, we must show that the n conditional statements p1 p2, p2 p3, , and Pn pi are true. The validity of this approach is based on the tautology