Question

On the set S of all real numbers, define a relation R = {(a, b):a ≤ b}. Show that R is transitive.

Answer 1

Given,

R = {(a, b):a ≤ b}

Reflexive Property

The Reflexive Property states that for every real number x, x = x.

Symmetric Property

The Symmetric Property states that for all real numbers x  and  y,

if  x = y, then y = x.

Transitive Property

The Transitive Property states that for all real numbers x ,y,  and  z,

if  x = y and y = z , then x = z

when, a = 1,b = 1,2

So, (1, 2),(2, 3) is possible, and (1, 3) is also possible as 1 ≤ 3.

Therefore, R is transitive.

Therefore, R is transitive.