Question 2. (7 Points: 3+2+2) (a) Prove that if a and y are rational numbers then x+y is rational. (b) Prove that if x is irrational and y is rational then r + y is irrational. (c) Provide either a proof or a counterexample for the following statement: "If x and y are irrational numbers then x+y is irrational."

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