PartI: Constructing Proofs (100 pt.) makea You must write down all proofs in acceptable mathematical language: make sure you mark the beginning and end of the proof, define all variables, use complete, grammatically correct sentences, and give a justification for each assertion (e.g., by definition of...). See lecture slides for examples. sentening and end of the prool, defnt Definitions: An integer n is even if and only if there exists an integer k such that n = 2k. An integer n is odd if and only if there exists an integer k such that n 2k + 1. Two integers have the same parity when they are both even or when they are both odd. Two integers have opposite parity when one is even and the other one is odd. An integer n is divisible by an integer d with d # 0, denoted d i n, if and only if there exists an integer k such that n -dk A real number r is rational if and only if there exist integers a and b with b # 0 such that r = a/b. For any real number x, the absolute value of x, denoted lx], is defined as follows xifx