Example

Example: Determining a Relation, Domain, and Range from a Mapping of Names and Birthdays

A mapping visually illustrates how elements in a domain pair with elements in a range using arrows. For example, consider a mapping that assigns individuals' names to their birthdays. By following the arrows from the names Alison, Penelope, June, Gregory, Geoffrey, Lauren, Stephen, Alice, Liz, and Danny to their corresponding birthdays, we can write this relation as a set of ordered pairs: {\{ (Alison, April 2525), (Penelope, May 2323), (June, August 22), (Gregory, September 1515), (Geoffrey, January 1212), (Lauren, May 1010), (Stephen, July 2424), (Alice, February 33), (Liz, August 22), (Danny, July 2424) }\}. The domain comprises all the xx-values, which is the set of all the names: {\{ Alison, Penelope, June, Gregory, Geoffrey, Lauren, Stephen, Alice, Liz, Danny }\}. The range contains all the yy-values, which is the set of all the unique birthdays: {\{ January 1212, February 33, April 2525, May 1010, May 2323, July 2424, August 22, September 1515 }\}. Note that even though multiple individuals may share a birthday (such as August 22 and July 2424), each distinct date is only listed once in the range.

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Updated 2026-04-24

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