State the direct proof, contrapositive proof, contradiction proof, and counterexample disproof for the following statements and prove the statements using one of the above techniques. 1. Suppose a, b e Z. If a(b + 3) is even then a is even or b is odd. Th [0,1] 3. For every integer n 5, 2n >n. 2. For every x E " sin x + cos x > 1. 2.277