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Problem 4 I 7 (36 points, 10 + 12 + 14) For each problem, provide strict math proof without any possible confusion or ambiguity. Do not just list math equations without convincing and enough math reasoning. (1) Prove the following claim using proof by contradiction: If 9: and n are both even, then m + n is even. (2) A rational number is a number that can be in the form '3 where p and q are integers (q 7e 0). Prove: For real numbers x and y, if x is rational and y is irrational, then x y is irrational. (3) Prove that for positive real numbers x and y, if x % y, then i + E > 2