Question: (a) Show that if x, y are rational numbers, then x + y and xy are rational numbers. (b) Prove that if x is a

(a) Show that if x, y are rational numbers, then x + y and xy are rational numbers.
(b) Prove that if x is a rational number and y is an irrational number, then x + y is an irrational number. If, in addition, x ≠ 0, then show that xy is an irrational number.

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