   Chapter 9.5, Problem 26ES ### 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 onto functions are there from a set with three from a set with three elements to a set with two elements? b. How many onto function are there from a set with three elements to a set with five elements? c. Howmany onto functions are there from a set with three elements to a set with three elements? d. How many onto functions are there from a set four elements to a set with two elements? e. How many onto functions are there from a set with four elements to a with three elements? Let c m , n be the number of onto functions from a set of m elements to a set of n elements, where m ≥ n ≥ 1. Find a formula relating c m , n to c m − 1 , n and c m − 1 ,   n − 1 .

To determine

(a)

To find:

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

Explanation

Given information:

The domain of the onto functions consist of three elements and the co-domain consists two elements.

Formula used:

Let f be a function of x. f is said to be onto if, and only if there exists an element in the domain for each element of the codomain of f

To determine

(b)

To find:

The number of onto functions from a set of three elements to a set of five elements.

To determine

(c)

To find:

The number of onto functions from a set of three elements to a set of three elements.

To determine

(d)

To find:

The number of the onto functions from four-element set to a two-elements set.

To determine

(e)

To find:

The number of the onto functions from four-element set to a three-elements set.

To determine

(f)

To find:

The formula relating cm1,n and cm1,n1 where cm,n is the number of onto functions from a set of m elements to a set of n elements.

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