   Chapter 9.2, Problem 21ES ### 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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# Suppose A is a set with m elements and B is a set with n elements. How many relations are there from A to B? How many function are there from A to B? What fraction of the relations from A to B are functions?

To determine

(a)

To find the number of number of relation from A to B.

Explanation

Given information:

Relation from set A to B.

Concept used:

A={a1,a2,.....,am} and B={b1,b2,.....,bn}

Calculation:

Any relation from A to B is a subset of the Cartesian product.

So, write a relation as the set of ordered pairs in which the first component comes from A and the second component from B.

The first component can be any element from the m elements of A and tile second is from any of the n elements of B.

If an element is present in an ordered pair, write it as 1 and the absence as 0

To determine

(b)

To find the number of functions are there from A to B.

To determine

(c)

The fraction of relations from A to B which are functions.

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