(a)

What is a relation on a set?

Expert Solution

Explanation of Solution

In mathematics, a binary relation on a set $A$ is a set of ordered pairs of elements of $A$ defined as

$R=a,ba,b∈A$ .

To determine

(b)

How many relations are there on a set with $n$ elements?

Expert Solution

Explanation of Solution

$S=a1,a2,a3,...,an$

Thus, there are $2n2$ relations on a set $S$ with $n$ elements.

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Chapter 9.6, Problem 67E

Chapter 9, Problem 2RQ

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Chapter 9 Solutions

DISCRETE MATHEMATICS LOOSELEAF

Ch. 9.1 - t the ordered pairs in the...Ch. 9.1 - a) List all the ordered pairs in the relation R =...Ch. 9.1 - each of these relations on the set {1, 2, 3, 4},...Ch. 9.1 - ermine whether the relationRon the set of all...Ch. 9.1 - ermine whether the relationRon the set of all Web...Ch. 9.1 - ermine whether the relationRon the set of all real...Ch. 9.1 - ermine whether the relationRon the set of all...Ch. 9.1 - w that the relationR=Oon a nonempty set S is...Ch. 9.1 - Show that the relationR=on the empty setS=is...Ch. 9.1 - e an example of a relation on a set that is a)...

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(a) What is a relation on a set?

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(a) What is a relation on a set?

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(b) How many relations are there on a set with n<m:math><m:mi>n</m:mi></m:math> elements?

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Chapter 9 Solutions

(a)

What is a relation on a set?

(b)

How many relations are there on a set with $n$ elements?