1. Give a proof by cases to prove that for all integers x, x 2 − x is an even integer. 2. Give a proof by contraposition that for a ∈ Z, if a 2 + 3 is odd, then a is even. 3. Give a proof by contradiction for real numbers a and b that a+b 2 < b ⇒ a < b. 4. Give a proof by contradiction that given integers j and k where j ≥ 2 that then j 6 | k ∨ j 6 | (k + 1).
