**Problem 1.**Is the set S = {[a]: [a] in Zm, gdc(a,m)=1 } is a group under operation of multiplication?

**Problem 2.**Are non-zero residue classes modulo p form a group with respect to multiplication?

**Problem 3.**Which of the following subsets of Z13 is a group with respect to multiplication?

a) {[1], [12]}

b) {[1], [2], [4], [6], [8], [10], [12]}

c) {[1], [5], [8], [12]}

P.S. As you solve these I would add more.