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Cartesian Product and Finite Sets and Algebra of Composition

I'd like to know the deductive techniques to prove each. A short and correct proof for each is all that is required.

OR please provide some help on how to solve them.

Please see the attached file for the fully formatted problems.

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Solution Summary

Cartesian Product and Finite Sets and Algebra of Compositions of Functions (10 Problems) are investigated. The solution is detailed and well presented.

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