   Chapter 9.5, Problem 25ES ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

#### Solutions

Chapter
Section ### Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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# a. How many one-of-one functions ant there from a set w ah three elements to a set with four elements? b. How many one-to-one functions are there from a set with three elements to a set with two elements? c. How many one-to-one functions are there from a set w uh three elements to a set with three elements? d. How many one-to-one functions are there from a set with three elements to a set with five elments? e. How marry one-to-one functions are there from a set with m elements to a set w uh n elements, where m ≤ n ?

To determine

(a)

To find:

The count of the one-to-one functions from three-element set to afour-elements set.

Explanation

Given information:

The domain of the one-to-one functions consist of three elements and the co-domain consists four elements.

Formula used:

The number of r combinations from n number of elements is given by the formula,

(nr)=n!(nr)!×r!

Let f be a function of x. f is said to be one-to-one if, and only if

f(x1)=f(x2) then x1=x2.

Calculation:

For being a one-to-one function, this functionneeds to satisfy the above condition

To determine

(b)

To find:

The number of one-to-one functions from a set of three elements to a set of two elements.

To determine

(c)

To find:

The number of one-to-one functions from a set of three elements to a set of three elements.

To determine

(d)

To find:

The number of the one-to-one functions from three-element set to a five-elements set.

To determine

(e)

To find:

The number of the one-to-one functions from m element set to n element set.

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