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.
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