Question: 4. For each of the given statement, do as required. (48 points, 12 each) (1). Prove by Direct Proof: Vn EZ, if 3 | (n2

4. For each of the given statement, do as required. (48 points, 12 each) (1). Prove by Direct Proof: "Vn EZ, if 3 | (n2 + 1), then 3 + (2n2 + 1)." (2). Prove by Contraposition: "Vk, m, n EZ, if k + 2m + 3n > 8, then k = 3,m = 2,orn > 2." (3). Disprove by a Counterexample: "Vm, n E Z, 2m + 3n is odd - m is even and n is odd."

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