Find a proof or exhibit a counterexample to each of the following statements.(a) [BB] 2x2...

Find a proof or exhibit a counterexample to each of the following statements.

(a) [BB] 2x2 4 − 3 y2 > 0 for all real numbers x and y.

(b) a an even integer an even integer.

(c) [BB] For each real number x, there exists a real number y such that xy = 1.

(d) If a and b are real numbers with a + b rational, then a and b are rational.

(e) [BB] a and b real numbers with ab rational → a and b rational.

(f) b2 − Aac > 0 and a ≠ 0 → p(x) = ax2 + bx + c has two distinct real roots.

(g) x2 ≥ x for all real numbers x.

(h) n2 ≥ n for all positive integers n.