Suppose a, b, and c denote integers and the following algebraic laws concerning inequalities are known:

Law A. (a > b and b > c) (a > c). (This is the transitivity law, which also holds if all > signs are replaced by the signs, or if exactly one of the > sign on the lefthand side replaced by .)

Law B.(a > b and c > 0) (ac > bc). The law is also valid if each > sign is replaced by the sign.

Law C.(a > b) (a+c > b+c), for any c. The law is also valid if each > sign is replaced by the sign.

Law D.(a > 0) (a < 0). Similarly, (a 0) (a 0).

LawE. ab>0 (a > 0 and b > 0) or (a < 0 and b < 0). The law is also valid if each > sign is replaced by the sign, and < replaced by .

Now use these laws and other appropriate definitions and theorems, and logical reasoning, to prove, or to disprove, each of the following statements, where all symbols denote integers (positive, zero, or negative). (Note: Recall that in the case of a disproof, you need to give a counter-example and explain why the example disproves the statement.)

(a) If a+b >0 and a 0, then b > 0.

(b) If a > 20 and b > 0,then a² > 2^b.

(c) If a > bc and c > b, then a > b².