Relations

The Definition of Relation

Mr. Budi has five children. They are Riska, Dimas, Candra, Dira, and Reni. Each of the children likes sports. Riska likes badminton and swimming. Dimas likes playing football. Candra also likes playing football. Dira and Reni like playing basketball and badminton.

Let Mr. Budi’s children be the members of Set A. Then Set A can be written as:

A = {Riska, Dimas, Candra, Dira, Reni}

On the other hand, the types of sports can be represented by Set B. Set B can be written as:

B = {badminton, swimming, basketball, football}

Considering the types of sports and Mr. Budi’s children, there is a regulation to relate between Set A and Set B. The regulation is “likes to play”.

Riska likes to play badminton and swimming.Dimas likes to play football.Candra likes to play football.Dira likes to play badminton and basketball.Reni likes to play badminton and basketball.

We see that there is a relationship between the members of Set A and the members of Set B. This is stated as a relation from Set A to Set B.

From the illustration above, we can devine relation as follows:

A relation from Set A to Set B is a regulation which connects the members of Set A to the members of Set B.

Definition of Relation

A relation can be expressed by three ways : 1. Arrow Diagram2. Cartesian Coordinates, and3. Set of Ordered Pairs.

Expressing a Relation of Two Sets Using an Arrow Diagram

A relation between two sets A and B can be represented by using an arrow diagram. The relation “likes to play” in Part A can be expressed as follows:

Consider the following situation: In the eighth grade of SMPN I Jakarta, there is a group of students consisting of 4 members: Ani, Adi, Ina, and Iman. Ani has a younger brother, Budi. Adi has two younger siblings, Surya and Hani. Ina doesn’t have any younger brothers or sisters, while Santi is the younger sister of Iman.Let P be the set of the study group members, and let Q be the set of their younger siblings. Then

P = {Ani, Adi, Ina, Iman} Q = {Budi, Hani, Surya, Santi}

The relation from the members of the set P to the set Q can be expressed as follows:

1. Can you find another relation between the members of Set P and Set Q above? Explain and illustrate the relation by an arrow diagram.

2. Give other examples of relations between the members of two sets that you know.