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

Solution:

The given set is A = {1, 2, 3}.

The smallest relation containing (1, 2) and (1, 3) which are reflexive and symmetric but not transitive is given by,

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

This is because relation R is reflexive as

{(1, 1), (2, 2), (3, 3)} ∈ R.

Relation R is symmetric as

{(1, 2), (2, 1)} ∈ R and {(1, 3)(3, 1)} ∈ R.

Relation R is transitive as

{(3, 1), (1, 2)} ∈ R but (3, 2) ∈ R.

Now,

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

then relation R will become transitive.

Hence,

the total number of desired relations is one.

The correct answer is A

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NCERT Solutions for Class 12 Maths - Chapter 1 Exercise ME Question 16

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 

Summary:

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