i need help with these questions 1-10

I. Suppose you wish to prove P Q using the contrapositive method. The structure of the proof would be (A) Suppose P and deduce Q (B) Suppose~P and deduceQ (C) SupposeQ and deduce~ P (D) Suppose~P andQ 2. Suppose you are trying to prove the following Proposition by using direct proof: 3 mod 4then n is Proposition 1 : If n is a positive integer such that n 2 mod 4 or n not a perfect square. Which of the followings should be the first sentence of your proof. (A) Suppose n is a positive integer such that n 2 mod 4 orn 3 mod 4. (B) Suppose n is a positive integer such that n2 mod and n3 mod 4 (C) Suppose n is not a perfect square (D) Suppose n is a perfect square. 3. Suppose you are trying to prove the following Proposition by using contrapositive proof 3 mod 4, then n is Proposition 1 : If n is a positive integer such that n 2 mod 4 or n not a perfect square Which of the followings should be the first sentence of your proof. (A) Suppose n is a positive integer such that n 2 mod 4 or n 3 mod 4. (B) Suppose n is a positive integer such that 2 mod 4 and n 3 mod4 n is not a perfect square C) Suppose (D) Suppose n is a perfect square. 4, Definition: A real valued function /(a) is called one-to-one ifr 12 for any real nurnbers z and r2, then f(n)f(x2). Suppose you are trying to prove that f(x)- isone-to-one by using contrapositive proof: Which of the followings should be the first sentence of your proof? (A) Assume r1x2 (C) Assume f(n)/(12) for some x1.r2 (D) Assume f(x) = f(x2) for some z1+12