Let A be the set of first five natural numbers and let R be a relation on A, defined by (x, y) ϵ R ↔ x ≤ y. Express R and R –1 as sets of ordered pairs. Find: dom (R –1 ) and range (R).

Question

Philoid · Accepted Answer

A = {1, 2, 3, 4, 5}

Since, x ≤ y

R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (2, 2), (2, 3) ,(2, 4), (2, 5), (3, 3), (3, 4), (3, 5), (4, 4), (4, 5), (5, 5) }

The domain of R is the set of first co-ordinates of R

Dom(R) = {1, 2, 3, 4, 5}

The range of R is the set of second co-ordinates of R

Range(R) = {1, 2, 3, 4, 5}

Let A be the set of first five natural numbers and let R be a relation on A, defined by (x, y) ϵ R ↔ x ≤ y.Express R and R–1 as sets of ordered pairs.Find: dom (R–1) and range (R).

Let A be the set of first five natural numbers and let R be a relation on A, defined by (x, y) ϵ R ↔ x ≤ y.
Express R and R^–1 as sets of ordered pairs.

Find: dom (R^–1) and range (R).