Part Il: Constructing proofs (60 pt.) You must write down all proofs in acceptable mathematical language: make sure you mark the beginning and end of the proof, define all variables, give a justification for every assertion (e.g., by definition of...), and use complete, grammatically correct sentences. Definitions: .An integer n is even if and only if there exists an integer k such that n-2k. An integer n is Two integers have the same parity when they are both even or when they are both odd. Two . An integer n is divisible by an integer d with d 0, denoted d | n, if and only if there exists an 0 such that odd if and only if there exists an integer k such that n-2k +1 integers have opposite parity when one is even and the other one is odd. integer k such that n-dk. A real number r is rational if and only if there exist integers a and b with b r-a/b. For any real number x, the absolute value of x, denoted i , is defined as follows: . x ifx 2