Part 1: 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.

Part I

A primary key is a unique identifier within a field or multiple fields in a database. The primary key allows a search to pull out specific records in a database. An example of this would be Property Tax Records with in a county government. A primary key in this example would be a Land Tax Map Number. This number would be the primary key because there would only be one property with this identifier so using this a primary key would allow only that property to be pulled up. Unlike using a name as a primary key because there could be multiple people with the same name in the database with multiple different properties so this would not work as a primary key.

Part II
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.

Part II

A{Feline, Canine, Reptile}
B{African Lion, Domestic Cat, Coyote, Labrador Retriever, Snapping Turtle, Alligator}

This is a relation because A has multiple relations within B, but when the domain and the range are switched this becomes a function because when B is the Domain each element in B matches with one element in A.