Question: Prove each implication by contradiction, (a) If x and y are positive numbers, then x + y x + y. (b) If x is

Prove each implication by contradiction,
(a) If x and y are positive numbers, then √x + y ≠ √x + √y.
(b) If x is irrational and y is rational, then x + y is irrational.
(c) If 13 people are selected, at least 2 have birthdays in the same month.

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