Maths. Section B1Relations and Functions

Let W denote the words in the English dictionary. Defined the relatio…

Let W denote the words in the English dictionary. Defined the relation R by : R = {(x, y) ∈ w × w the words x and y have at least one letter in common}. Then R is :

Answer & explanation

Correct answer: option 2

Clearly (x, x) ∈ R ∀ x ∈ w. So, R is reflexive

Let (x, y) ∈ R, then (y, x) ∈ R as x and y have at least one letter in common. So, R is symmetric.

But R is not transitive for example

Let x = DELHI, y = DWARKA and z = PARK

then (x, y) ∈ R and (y, x) ∈ R but (x, z) ∉ R.