Question

Which of the following is an identity relation on the set $A=\{a,b,c\}$?

• A. $R=\left\{\right(a,a),(b,b\left)\right\}$
• B. $R=\left\{\right(a,b),(b,c\left)\right\}$
• C. $R=\left\{\right(a,b),(b,c),(c,a\left)\right\}$
• D. $R=\left\{\right(a,a),(b,b),(c,c\left)\right\}$

Answer 1

The correct option is D $R=\left\{\right(a,a),(b,b),(c,c\left)\right\}$

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