Question

If $A=\{1,2,3\}$, then the number of equivalence relation containing$(1,2)$ is

• A. $1$
• B. $2$
• C. $3$
• D. $8$

Answer 1

The correct option is B

$2$

Explanation for the correct option:

Finding number equivalence relation.

Given,

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

Relation,

R =$\left\{\right(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3\left)\right\}$

R₁=$\left\{\right(1,1),(2,2),(3,3),(1,2),(2,1\left)\right\}$

R₂=$\left\{\right(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2),(1,3),(3,1\left)\right\}$

There is only two containing equivalence relation $(1,2)$
Hence, correct option is $\mathbf{\left(}\mathit{B}\mathbf{\right)}\mathbf{.}$