INTRODUCTION TO ABSTRACT ALGEBRA I

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INTRODUCTION TO ABSTRACT ALGEBRA I Instructions and Guidelines:  No late assignments will be accepted  Full marks will be awarded for showing all steps and working upon arrival of the solution  Students are reminded that although group discussion is advised, this is an indiv idual assignment that is worth 10 % of the final grade 1. Exhibit the 15 proper subsets of You didn't specify the set for which the proper subsets are needed. A proper subset of a set is any subset that is not equal to the original set. If you provide the set SSS, I can give you the 15 proper subsets. For example, for S={1,2,3,4}S = \ {1, 2, 3, 4 \ }S={1,2,3,4}, the proper subsets would be all subsets of SSS, except for SSS itself. The subsets would be: • {} • {1} \ {1 \ }{1} • {2} \ {2 \ }{2} • {3} \ {3 \ }{3} • {4} \ {4 \ }{4} • {1,2} \ {1, 2 \ }{1,2} • {1,3} \ {1, 3 \ }{1,3} • {1,4} \ {1, 4 \ }{1,4} • {2,3} \ {2, 3 \ }{2,3} • {2,4} \ {2, 4 \ }{2,4} • {3,4} \ {3, 4 \ }{3,4} • {1,2,3} \ {1, 2, 3 \ }{1,2,3} • {1,2,4} \ {1, 2, 4 \ }{1,2,4} • {1,3,4} \ {1, 3, 4 \ }{1,3,4} • {2,3,4} \ {2, 3, 4 \ }{2,3,4} 2. Prove that
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