Question: Prove the following using the specified technique: (1) Let x and y be two real numbers such that x + y is rational. Prove by

Prove the following using the specified technique:

(1) Let x and y be two real numbers such that x + y is rational. Prove by contrapositive that if x is irrational,

then x y is irrational.

(2) Prove by contradiction that for any positive two real numbers, x and y, if x y 50, then either x < 8 or y < 8.

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