From the statements below, construct a proof of contradiction to show that if m and n are integers such that mn=1, then either m=1 and n=1, or else m=1 and n=1. Step 1 [ Choose ] Let q be m=1 and n=1, or else m=1 and n=1. Step 2 Let p be m and n are integers such that mn=1, so not p is mn does not equal 1 . Since mn must equal 1 and 1 has no factor other than 1 or 1,m and n must equal 1 or -1 . So with, p and not q,mn=1 and neither m nor n equal 1 or -1 . Let p be m and n are integers such that mn=1. This is a contradiction, so m and n must equal 1 or -1 . Let q be m=1 and n=1, or else m=1 and n=1, so not q is m and n do not equal 1 or This proves m and n equal 1 or -1 . Step 4 So with, not p and q,mn does not equal 1 and m and n equal 1 or -1 . Since mn does not equal 1 , so m or n can equal 1 or -1 . Step 5