Question

$A=\{5,7,9\},$ then which of the following is the identity relation on $A$?

• A. $R_1=\left\{\right(5,5),(7,7),(9,9),(5,7),(7,9),(9,5\left)\right\}$
• B. $R_2=\left\{\right(9,7),(7,5),(5,9),(5,5),(7,7),(9,9\left)\right\}$
• C. $R_3=\left\{\right(5,5),(7,7),(9,9\left)\right\}$
• D. $R_4=\left\{\right(5,7),(7,9),(9,5\left)\right\}$

Answer 1

The correct option is C $R_3=\left\{\right(5,5),(7,7),(9,9\left)\right\}$

Let $A$ be any set. Then the relation $R=\left\{\right(x,x):x\in A\}$ on $A$ is called the identity relation on $A.$
i.e., for any identity relation, each element is related to itself only in the given relation.
$R_3=\left\{\right(5,5),(7,7),(9,9\left)\right\}$