Question

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 1

The correct option is A $1$

$A=\{1,2,3\}$

Relation containing $(1,2)$ and $(1,3)$

For symmetricity, $(1,2),(2,1),(1,3)$ and $(3,1)$ must be included.

For reflexivity,$(1,1),(2,2),(3,3)$ must be included.

$\Rightarrow$ Only one set is there $R=\left\{\right(1,1),(1,2),(1,3),(2,2),(2,1),(3,3),(3,1\left)\right\}$

$\Rightarrow$ Answer is $1$.