Create a mathematical system with two binary operations.
Chapter 10, Problem 10.1.41(choose chapter or problem)
Create a mathematical system with two binary operations. Select a set of elements and two binary operations so that one binary operation with the set of elements meets the requirements for a group and the other binary operation does not. Explain why the one binary operation with the set of elements is a group. For the other binary operation and the set of elements, find counterexamples to show that it is not a group.
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