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Relations

Relations. 2.1. A. The Definition of Relation.

sigourney-buckley
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Relations

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  1. Relations 2.1 A 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.

  2. Let Mr. Budi’s children be the members of Set A. Then Set A can be writtenas: 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}

  3. 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”. Riskalikes to play badminton and swimming. Dimas likes to playfootball. Candralikes to play football. Diralikes to play badminton and basketball. Reni likes to play badminton and basketball. We see that there is a relationship between themembers of Set A and the members of Set B. This is stated as a relation from Set A to Set B.

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

  5. A relation can be expressed by three ways : • Arrow Diagram • Cartesian Coordinates, and • Set of Ordered Pairs.

  6. B 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:

  7. 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}

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

  9. Problem 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. • Give other examples of relations between the members of two sets that you know.

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