Prove that the following propositions are ture.

The procedure of proof should follow the following format. The answer should like that.

Example

Proposition: For all integers a,b,c, if a > b and c

Proof.

(1)Let a,b,c be arbitrary integers, and suppose that a > b and c

(2)From (1), we know that a > b, so a - b > 0.

(3)From arithmetic, we know that a positive number times a negative number is negative.From (2), (a-b) is positive. From (1), c is negative. So (a-b)c

(4)But (a-b)c = ac-bc. From (3), we know (a-b)c

(5)Since ac-bc (e) For every integer n, 3n 2 is even if and only if n 5 is odd. (f) For any integers a and y, max(x, y) + min(x, y) -y Clarification: max is a function that returns the largest value, min is a function that returns the smallest value. Clarification: the interval (r1,) consists of all real numbers r such that r > r- 1 and a