Prove each of the following statements using a direct proof a) 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.) For any positive real numbers, x and y z + y y If x is a real number and x s 3, then 12-7x+x220. The product of two odd integers is an odd integer If r and s are rational numbers, then the product of r and s is a rational number