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What Is a Relation?
A relation pairs up elements from one set with elements from another.
Pairs of Values
An ordered pair (, ) links an input to an output . A relation is simply a collection of such pairs. Relations can be shown as a list of pairs, a table, or a mapping diagram with arrows from inputs to outputs.
A relation places no restriction on how many outputs one input can have. The next lesson introduces a special, more useful kind of relation: the function.
Example 1 — reading a relation
The relation R = {(, ), (, ), (, ), (, )} connects inputs to outputs.
- Input connects to output .
- Input connects to two outputs: and .
- Input connects to output .
Practice
In the relation {(, ), (, ), (, )}, how many outputs does input have?
More lessons in Sets and Functions · Next: What Is a Function? · Previous: Three-Set Venn Diagrams