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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 ), (Penelope, May ), (June, August ), (Gregory, September ), (Geoffrey, January ), (Lauren, May ), (Stephen, July ), (Alice, February ), (Liz, August ), (Danny, July ) . The domain comprises all the -values, which is the set of all the names: Alison, Penelope, June, Gregory, Geoffrey, Lauren, Stephen, Alice, Liz, Danny . The range contains all the -values, which is the set of all the unique birthdays: January , February , April , May , May , July , August , September . Note that even though multiple individuals may share a birthday (such as August and July ), each distinct date is only listed once in the range.
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