Research the term primary key. Discuss what this means in the context of functions and relations. Describe an example of the use of a primary key.
Consider the example of the states of the United States and the senators of the United States. If you consider the set of states as a domain and the set of senators as a range, you can establish a relation based on associations between the senators and the states. This relation would not be a function because each state corresponds to more than one senator. However, if you reverse the roles of the domain and range, then the relation is a function because each senator is associated with only one state.
Make up your own example of 2 real-world sets – each with more than one element – and describe how the elements of the different sets can be paired, such that
•if one set is considered the domain and the other the range, then the relation is not a function, and
•if the roles (domain and range) of the two sets are reversed, then the relation is a function.