Problem

Let x, y, and z be integers. Write a proof by contraposition to show that (a) if x...

Let x, y, and z be integers. Write a proof by contraposition to show that

(a) if x is even, then x + 1 is odd.

(b) if x is odd, then x + 2 is odd.

(c) if x2 is not divisible by 4, then x is odd.

(d) if xy is even, then either x or y is even.

(e) if x + y is even, then x and y have the same parity.

(f) if xy is odd, then both x and y are odd.

(g) if 8 does not divide x2 − 1, then x is even.

(h) if x does not divide yz, then x does not divide z.

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Solutions For Problems in Chapter 1.5