Suppose x and y are real numbers. Recall that a real number m is rational iff m = p/q, where p and q are integers and q ≠ 0. If a real number is not rational, then it is irrational. Prove the...

Suppose x and y are real numbers. Recall that a real number m is rational iff m = p/q, where p and q are integers and q ≠ 0. If a real number is not rational, then it is irrational. Prove the following. [You may use the fact that the sum of integers and the product of integers are again integers.]

(a) If x is rational and y is rational, then x + y is rational.

(b) If x is rational and y is rational, then xy is rational.

(c) If x is rational and y is irrational, then x + y is irrational