Prove each of the following statements using a direct proof. If n is an odd integer, then n2 is an odd integer. (Note: the definition of an odd integer is an integer that can be expressed as 2k + 1, where k is an integer) (b) For any positive real numbers, x and y ty2vy (c) If x is a real number and x s 3, then 12-7x +x220. (d) The product of two odd integers is an odd integer. (e) If r and s are rational numbers, then the product of r and s is a rational number