Consider the following theorem. Theorem: The sum of any even integer and any odd integer is odd Six of the sentences in the following scrambled list can be used to prove the theorem
Suppose m is any even integer and n is any odd integer.
By definition of even and odd, there is an integer r such that m = 2r and n 2r+ 1.
By substitution and algebra, m n = 2r + (2s 1) 2(r s) 1.
Let mn be any odd integer
So by definition of even, t is even.
Let t = r + s. Then, t is an integer because it is a sum of integers.
By substitution, m + n = 2t + 1
Hence, the sum is twice an integer plus one. So by definition of odd,By definition of even and odd,there are integers r and s such that m = 2r and n = 2s + 1.