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 Prove that the following propositions are true: b) For any two integers and y with different parity (one is even and one is odd), x - y is odd (c) For every integer n, 6n 19 is odd (d) If n is a positive integer and n s4, then n 1)323" (e) For every integer n, 3n 2 is even if and only if n +5 is odd (f) For any integers x and y, max(x,y) + min(x,y) = x + y. rygest talue, min is function that returns the smallest value. (g) If a real number r is not an integer, then there is an integer n in the interval (r- 1,r) Clarification: the interval (r 1, r) consists of all real numbers x such that ax > r- 1 and x