Question

Which of the following is/are not 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

Answer: (A), (B), (C)

The correct options are
A $R=\left\{\right(a,a),(b,b\left)\right\}$
B $R=\left\{\right(a,b),(b,c\left)\right\}$
C $R=\left\{\right(a,b),(b,c),(c,a\left)\right\}$

For identity relation, each element is related to itself only in the given relation.
Hence, $R=\left\{\right(a,a),(b,b),(c,c\left)\right\}$ is the only identity relation.