Each statement below involves odd and even integers. An odd integer is an integer that can be expressed as 2/+1,where k is an integer. An even integer is an integer that can be expressed as 2k, where is an integer. Prove each of the following statements using a direct proof. (a) The sum of an odd and an even integer is odd.
(b) The sum of two odd integers is an even integer
(c) The square of an odd integer is an odd integer
(d) The product of two odd integers is an odd integer.