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Chapter 12: Problem 2

What is the domain of a relation?

Short Answer

Expert verified
The domain of a relation is the set of all input values (x-values) of the ordered pairs in the relation. For example, if we have the relation R = \(\{(1,2), (2,4), (3,6), (4,8)\}\), the domain of this relation would be Domain(R) = \(\{1, 2, 3, 4\}\).

Step by step solution

01

1. Defining Domain of a Relation

In mathematics, a relation is a set of ordered pairs, where each ordered pair consists of an input value and an output value (usually represented as \((x,y)\) or \((a,b)\)). The domain of a relation is the set of all input values (x-values). It is essential to understand the domain, as it represents all the possible values for a function or relation's input.
02

2. Example of a Relation and Finding its Domain

Let's say we have a relation represented by the following set of ordered pairs: R = \(\{(1,2), (2,4), (3,6), (4,8)\}\) This relation consists of 4 ordered pairs, each with an input value and an output value. To find the domain, we simply list all the input values (x-values) without repetition: Domain(R) = \(\{1, 2, 3, 4\}\) In this case, the domain of relation R includes the values 1, 2, 3, and 4.

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