1. Set Partition [10%) Let Z3-10], [1], [2]} denote the set of equivalence classes modulo 3. Prove that [O] n [11-0, [0in 2-0. and [1] n [2]-. Number Theory[10%) Prove that if n Z t n2 (mod 4) 2, hen n2-0 (mod 4) or 3. Number Theory[10%]. Prove that if a,b,c and m are integers such that m 2, c > 0, and a-b (mod m), then ac-be (mod mc). 4, Division Theorem [10%]. Prove that every prime number except 2 and 3 is of form 6k + 1 or 6k + 5 for some k Z. Hint note n-6 and apply division theorem