Please answer the three parts. Provide justification as well and name of proof. Thanks!

Part l: Constructing Proofs (100 pt.) begimingand end or e prel alifaiahi You must write down all proofs in accentable 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. 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