Answers must be correct. Or else it will be flagged. All of these sub parts need to be answered with step by step process showing all work and reasoning.

You must use Discrete Mathematics Notation

Answers must be correct. Or else it will be flagged. All of these sub parts need to be answered with step by step process showing all work and reasoning.

You must use Discrete Mathematics Notation

1.A. Direct proof . Give a direct proof of each of the following two statements . If an integer z is odd, then 3 is odd. . Let a, b, cE Z. If alb and alc, then al (b c) ais he lcalig weojaled salenert 3m E 2, 3n E Z, (m and n are perfect squares) ^ (mn is not a perfect square) Hint: recall that ~ (PA ~ Q) Q. 1.B. Proof by contrapositive Give a proof by contrapositive of the following statement. Let n be an integer. Then 5t implies 51m 1.C. Proof by cases Give a proof by cases of the following statement If two integers have the same parity, then their sum is even. 1.D Proof by contradiction Give a proof by contradiction of the following statement lf A and B are sets, then A n(B-A) = 0