(a) how many one-to-one functions are there from a set with four elements to a set with five elements? there are choices for where to send the first element of the domain, choices for where to send the second element of the domain, and so forth. thus, the total number of one-to-one functions is . (b) how many one-to-one functions are there from a set with four elements to a set with three elements? (c) how many one-to-one functions are there from a set with four elements to a set with four elements? (d) how many one-to-one functions are there from a set with four elements to a set with six elements?

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joaobezerra joaobezerra · Answer 1 · 2022-11-25T12:41:12+01:00

The number of one-to-one functions is given as follows:

a) Four to five: 120.

b) Four to three: 24.

c) Four to four: 24.

d) Four to six: 360.

A one-to-one function is a function in which each element of the output is mapped to at most one element of the input.

The permutation formula is used to give the number of possible functions in this problem, which is given as follows:

[tex]P_{(n,x)} = \frac{n!}{(n-x)!}[/tex]

Giving the number of permutations of x elements from a set of n elements.

Hence the amount for item a is given as follows:

5!/(5 - 4)! = 5! = 120.

For item b, the amount is given as follows:

4!/(4 - 3)! = 4! = 24.

For item c, the amount is given as follows:

4!/(4 - 4)! = 4! = 24.

As the factorial of zero is of 1.

For item d, the amount is given as follows:

6!/(6 - 4)! = 6!/2! = 360.

More can be learned about one-to-one functions at https://brainly.com/question/15271413

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