# We can work on A relationship

What is a relationship, and what three types of relationships exist? Provide a real world/application example for each of the three types of relationships.

A relationship is a connection or association between two or more entities. In mathematics, a relationship is a rule that maps elements from one set to elements of another set.

There are three main types of relationships:

• Functional relationships:Â A functional relationship is a relationship where each element in the first set is associated with exactly one element in the second set. For example, the relationship between a person’s name and their age is a functional relationship.
• Non-functional relationships:Â A non-functional relationship is a relationship where each element in the first set may be associated with zero, one, or more elements in the second set. For example, the relationship between a person’s name and their friends is a non-functional relationship.

• Equivalence relationships:Â An equivalence relationship is a relationship where each element in the first set is associated with exactly the same elements in the second set. For example, the relationship between a person’s name and their social security number is an equivalence relationship.

Here are some real world examples of each type of relationship:

• Functional relationship:Â The relationship between a person’s name and their age is a functional relationship. Each person has a unique name and a unique age.
• Non-functional relationship:Â The relationship between a person’s name and their friends is a non-functional relationship. A person may have zero, one, or more friends.
• Equivalence relationship:Â The relationship between a person’s name and their social security number is an equivalence relationship. Each person has a unique social security number, and no two people have the same social security number.