If-Y-is-a-non-void-set-define-Y-T-to-be-the-collection-of-all-functions-with-domain-T-and-range-Y-Show-that-if-T-and-Y-are-finite-sets-with-m-and-n-elements-then-Y-T-has-n-m-elements-

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Question Number 21491 by dioph last updated on 24/Sep/17

If Y is a non−void set, define Y^T to be the collection of all functions with domain T and range Y. Show that if T and Y are finite sets with m and n elements, then Y^T has n^m elements.

$$\mathrm{If}\:{Y}\:\mathrm{is}\:\mathrm{a}\:\mathrm{non}−\mathrm{void}\:\mathrm{set},\:\mathrm{define}\:{Y}^{{T}} \:\mathrm{to}\:\mathrm{be} \\ $$$$\mathrm{the}\:\mathrm{collection}\:\mathrm{of}\:\mathrm{all}\:\mathrm{functions}\:\mathrm{with} \\ $$$$\mathrm{domain}\:{T}\:\mathrm{and}\:\mathrm{range}\:{Y}.\:\mathrm{Show}\:\mathrm{that} \\ $$$$\mathrm{if}\:{T}\:\mathrm{and}\:{Y}\:\mathrm{are}\:\mathrm{finite}\:\mathrm{sets}\:\mathrm{with}\:{m}\:\mathrm{and} \\ $$$${n}\:\mathrm{elements},\:\mathrm{then}\:{Y}^{{T}} \:\mathrm{has}\:{n}^{{m}} \:\mathrm{elements}. \\ $$

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If-Y-is-a-non-void-set-define-Y-T-to-be-the-collection-of-all-functions-with-domain-T-and-range-Y-Show-that-if-T-and-Y-are-finite-sets-with-m-and-n-elements-then-Y-T-has-n-m-elements-

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