Understanding Relations: Definition and Expression Methods

1. Relation

2. What will you learn? Definition of relation Expressing relation

3. Definition of Relation Dina likes to eat strawberry and watermelon . Ani likes to eat pineapple Cika likes to eat watermelon If set A = { Dina, Ani, Cika} and set B = {strawberry, pineapple, watermelon} A relation among the elements of the set A and the elements of set B can be built. The relation from set A to set B is “likes to eat”

4. Definition of Relation Relation from set A to set B is a rule for pairing the elements of the set A with the elements of the set B.

5. Expressing Relations • Arrow Diagrams • Cartesian Diagrams • Sets of Ordered Pairs

6. Arrow Diagrams A Likes to eat B Dina Ani Cika Strawberry Pineapple Watermelon

7. Cartesian Diagrams B Watermelon Pineapple Strawberry A Dina Ani Cika

8. Sets of Ordered Pairs {(Dina,strawberry), (Dina,watermelon), (Ani,pineapple),(Cika, watermelon)}

9. Domain, Codomain, Range On previous example, Set A is domain Set B is codomain The elements of B (codomain) which haspair fromdomain make the set called range

10. Example Given : Set A = { 2, 3, 4} Set B = { 2, 4, 6} “less than” is the relation that connect the set A to the set B. Express those relations by: 1. Arrow Diagram 2. Cartesian Diagram 3. Sets of Ordered Pairs

11. A B 2 3 4 2 4 6 Answer Arrow diagram Less than

12. Cartesian diagram B 6 4 2 A 2 3 4 Sets of Ordered Pairs {(2, 4), (2,6), (3, 4), (3, 6), (4, 6)}