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A Transition to Advanced Mathematics | 7th Edition | ISBN: 9780495562023 | Authors: Douglas Smith, Maurice Eggen, Richard St. Andre
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Suppose that set A has m elements and set B has n elements. We have seenthat has mn

Chapter 4, Problem 17

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QUESTION:

Suppose that set A has m elements and set B has n elements. We have seenthat has mn elements and that there are relations from A to B. Findthe number of relations from A to B that are(a) functions from A to B.(b) functions with one element in the domain. (c) functions with two elements in the domain.(d) functions whose domain is a subset of A.

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QUESTION:

Suppose that set A has m elements and set B has n elements. We have seenthat has mn elements and that there are relations from A to B. Findthe number of relations from A to B that are(a) functions from A to B.(b) functions with one element in the domain. (c) functions with two elements in the domain.(d) functions whose domain is a subset of A.

ANSWER:

Step 1 of 4

Given that there are two set  and  having number of elements  and , respectively.

(a)

For a function to exist from  to , each and every element of set  must be related to exactly one element in . Each such combination will give birth to a separate function.

Therefore, the total number of possible functions from  to  will be equal to the number of all possible distinct combinations of  elements of set  and  elements of set .

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