Construct a proof for the statement by selecting sentences from the following scrambled list and putting them in the correct order. Thus, a + b = 2k, where k is an integer. By substitution and algebra, a + b = (2r) + (2s) = 2(2r + 2s). Let k = 2(r + s) + 2(r + s) + 1. Then k is an integer because sums and products of integers are integers. Let k = 2r + 2s. Then k is an integer because sums and products of integers are integers. By definition of odd integer, a = 2r + 1 and b = 2s + 1 for some integers r and s. Suppose a and b are any integers. By substitution and algebra, a + b = (2r + 1) + (2s + 1) = 2[2(r + s) + 2(r + s) + 1]. Suppose a and b are any odd integers. By definition of odd integer, a = 2r + 1 and b = 2r + 1 for any integers r and s. Hence a + b is even by definition of even