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INTRODUCTION TO ABSTRACT ALGEBRA I

An introductory exploration of abstract algebra concepts in mathematics.

Lily Green
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INTRODUCTION TO ABSTRACT ALGEBRA IInstructions and Guidelines:No late assignments will be acceptedFull marks will be awarded for showing all steps and working upon arrivalof the solutionStudents are reminded that although group discussion is advised, this is anindividual assignment that is worth 10% of the final grade1.Exhibit the 15 proper subsets ofYou didn't specify the set for which the proper subsets are needed. A propersubset of a set is any subset that is not equal to the original set. If youprovide 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 propersubsets would be all subsets of SSS, except for SSS itself. The subsetswould 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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