2. Prove that the following propositions are false:

(a) For all real numbers a and b, if a < b then a 4 < b4 .

(b) For all integers m and n, if 2m + n is odd, then m and n are both odd.

(c) For all integers x and y, (x + y) 2 = x 2 + y 2 .

(d) n Z, a Z, a n = (a) n