a. Rewrite the following theorem in the form _______ if______then______ b. Fill in the...

a. Rewrite the following theorem in the form _______ if______then______

b. Fill in the blanks in the proof.

Theorem: The sum of any even integer and any odd integer is odd.

Proof: Suppose in is any even integer and n is___(a)_. By definition of even, m = 2r for some ____(b)___ and by definition of odd, n = 2s + 1 for some integer s. By substitution and algebra. m + n = Since r and s are both integers, so is their sum r + s. Hence m + n has the form 2 . (some integer) + 1, and so __(d)__ by definition of odd.