Question

A relation in a set 'A' is known as empty relation:-

Options

• If no element of 'A' is related to any element of 'A'

• If all element of A is related to any element of 'A'

• If all elements of A is related to all element of 'A'

• None of the above

Answer 1

If no element of 'A' is related to any element of 'A'

Explanation:

Empty Relation:- An empty relation in a set 'A' is one in which no element of 'A' is related to any element of A, i.e.,

R = `phi` CA × A

e.g. Let the set A = {1, 2, 3, 4, 5} and R is given by

R = {(a, b) : a – b = 20}

There is no pair (a, b) that meets the condition.

a – b = 20

⇒ The empty relation is the relation 'R.'