Mathematics Problems - Relations and functions
If X = {2, 5} and Y = {1, 4, 7} and R is a relation from X to Y where "a R b" means "a < b" for every a ∈ X and b ∈ Y, state the relation R and represent it by an arrow diagram and by a Cartesian diagram.
Solution
∵ 2 is not less than 1
∴ (2, 1) ∉ R
∵ 2 < 4
∴ (2, 4) ∈ R
∵ 2 < 7
∴ (2, 7) ∈ R
∵ 5 is not less than 1
∴ (5, 1) ∉ R
∵ 5 is not less than 4
∴ (5, 4) ∉ R
∵ 5 < 7
∴ (5, 7) ∈ R
∴ The relation R = {(2, 4), (2, 7), (5, 7)}
The following figures represent the arrow diagram and the Cartesian diagram of this relation:
The Arrow Diagram
X
2
5
Y
1
4
7
The Cartesian Diagram
X
Y
2
5
1
4
7