You may use a calculator on this quiz. You may not use a cell phone or computer. To receive full credit please show your work carefully and give justifications for your answers. If you find that you are spending a lot of time on one problem, leave it blank and move on to the next.

- (10 points) Evaluate: 26 mod 11 =
- (20 points) For the equivalence relation defined by aRb if a mod 11 = b mod
11, what is the equivalence class of 7?
- The set {1, 2, 3, 4, 5, 6} together with the
operation "multiplication mod 7" forms a group G.
a) (10 pts) What is the identity element in this group?

- (20 points) List the properties that a set G together with an operation *
must have in order to be a group, or else give the definition of a group.
- (20 points) Consider the set {1, 2, 3, 4, 5, 6, 7} and the operation
"multiplication mod 8". Prove or disprove that these combine to make a
group.