Suppose x and y are real numbers. Prove or give a counterexample.
(a) If x is irrational and y is irrational, then x + y is irrational.
(b) lf x + y is irrational, then x is irrational or y is irrational.
(c) If x is irrational and y is irrational, then xy is irrational.
(d) If xy is irrational, then x is irrational or y is irrational.
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