EXERCISE 2.7.1: Proofs by cases - statements about numbers.

Prove each statement.

(a) For every real number x, x² > 0.

(b) For every integer n, n² > n.

(c) If x is a real number such that x² + 2x - 3 <0, then -3 < x < 1.

(d) If x is a real number such that ² -3x -10 <0, then -2 < x < 5.

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