Relations and functions

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:

Created with Mr. Ayman Hassan for Math Egypt Lovers