Question

Express the relation S in the table as a set of ordered pairs. Then identify the domain and range

Answer 1

Recall that a relation as a set of ordered pairs, is the set of points of the form:

`(x,y)`

such that x is related to y.

Now, from the given table we get that:

3 is related to 7,

5 is related to 11,

7 is related to 15,

9 is related to 19,

11 is related to 23.

Therefore, the relation is:

`S=\mleft\lbrace(3,7),(5,11),(7,15),(9,19),(11,23)\mright\rbrace\text{.}`

Now, recall that, for any relation as a set of ordered pairs, the set of all first components of the ordered pairs is called the domain and the set of all second components is called the range.

Therefore, the domain of the given relation is:

`\text{Domain}=\mleft\lbrace3,5,7,9,11\mright\rbrace\text{.}`

And its range is:

`\text{Range}=\mleft\lbrace7,11,15,19,23\mright\rbrace\text{.}`

Answer:

`\begin{gathered} S=\lbrace(3,7),(5,11),(7,15),(9,19),(11,23)\rbrace, \\ \text{Domain}=\lbrace3,5,7,9,11\rbrace, \\ \text{Range}=\lbrace7,11,15,19,23\rbrace\text{.} \end{gathered}`