For each of the following statements, either prove it is true or give a counterexample to show

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For each of the following statements, either prove it is true or give a counterexample to show it is false.

(a) The product of two rational numbers is always rational.

(b) The product of two irrational numbers is always irrational.

(c) The product of two irrational numbers is always rational.

(d) The product of a non-zero rational and an irrational is always irrational.

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