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Exercise 2.5.1: Proofs by cases. Prove each statement. Give some explanation of your answer (b) If...

Exercise 2.5.1: Proofs by cases.

Prove each statement. Give some explanation of your answer

(b)

If x and y are real numbers, then max(x, y) + min(x, y) = x + y.

(c)

If integers x and y have the same parity, then x + y is even.

The parity of a number tells whether the number is odd or even. If x and y have the same parity, they are either both even or both odd.

(d)

For any real number x, |x| ≥ 0.

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