Math 3130 Midterm: Due Wednesday October 21 in Class Remember to show your work! Summary: Math 3130 Midterm: Due Wednesday October 21 in Class Remember to show your work! Directions This is a take home, open notes test. There are eight problems on the test. You must answer carefully and completely any five of the problems. You answer must be your own; you are free to discuss problems with other students but must write up your own answers. Excessive similarity of answers will be noted and dealt with appropriately. Problem 1 Give the Cayley table of (Z 36, ·) and determine the order of each element. Problem 2 Prove that (P({a, b, c}), ) is a group, give the Cayley table, determine if the group is commutative, and give the order of each element. Problem 3 Compute GCD(56, 91) = 91x + 56y using the Euclidean algorithm and solving for x and y by back substitution through the Euclidean algorithm. Problem 4 Let A be a group with two elements and so that A consists of all possible products in any order of and . If and satisfy the following relations: 3 = 3 = ()2 = e Collections: Mathematics