Consider the proof below. theorem: let n be an integer. if n is odd, then n is odd. proof: let n be an integer. assume n is odd and n is even. then there is some integer k such that n=2k. then n2=(2k)2 = 4k which is even. therefore, n must be odd. pi is the proof valid, and which type of proof is used? the proof is valid, and proof by contradiction is used. the proof is not valid, and a direct proof is used. the proof is not valid, and a contradiction proof is used. the proof is valid, and a direct proof is used.