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Cartesian Product and Finite Sets and Algebra of Composition

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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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Problem #2
Proof:
(a) When , we have by definition. Assume the statement is true for , that is for all , then for , if , then by definition, we have

This implies that and . By the assumption,
for all ,
Thus for all . So the ...

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