Q. 164.4( 8 Votes )

# Let A = {1, 2, 3}. Then number of relations containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is

A. 1

B. 2

C. 3

D. 4

Answer :

This is because relation R is reflexive as (1, 1), (2, 2), (3, 3) ϵ R.

Relation R is symmetric as (1, 2), (2, 1) ϵ R and (1, 3), (3, 1) ϵ R.

But relation R is not transitive as (3, 1), (1, 2) ϵ R but (3, 2) R.

Now, if we add any one of the two pairs (3, 2) and (2, 3) (or both) to relation R,

Then, relation R will become transitive.

Therefore, the total number of desired relations is one.

Rate this question :

Fill in the blanks in each of the

Let the relation R be defined on the set

A = {1, 2, 3, 4, 5} by R = {(a, b) : |a^{2} – b^{2}| < 8}. Then R is given by _______.

State True or False for the statements

Every relation which is symmetric and transitive is also reflexive.

Mathematics - ExemplarState True or False for the statements

Let R = {(3, 1), (1, 3), (3, 3)} be a relation defined on the set A = {1, 2, 3}. Then R is symmetric, transitive but not reflexive.

Mathematics - ExemplarState True or False for the statements

An integer m is said to be related to another integer n if m is a integral multiple of n. This relation in Z is reflexive, symmetric and transitive.

Mathematics - Exemplar