Prove the following statement by contraposition. Let x be an integer. "If x^2 − x + 1 is even, then x is odd". Make sure that your proof makes appropriate use of definitions 1.5 and 1.6.
(Definition 1.5: An even integer is defined as an integer that can be expressed in the form 2k, where k is an integer.
Definition 1.6: An odd integer is defined as an integer that can be expressed in the form 2k + 1, where k is an integer.)