Types of Relations – 22 January 2025 (Shift 1)

Question ID: #108
JEE Main22 January Shift 1, 2025Algebra

The number of non-empty equivalence relations on the set $\{1, 2, 3\}$ is:

  • (1) 6
  • (2) 7
  • (3) 5
  • (4) 4

Solution:

$ \displaystyle
\begin{aligned}
& R_1 = \{(1,1), (2,2), (3,3)\} \\
& R_2 = \{(1,1), (2,2), (3,3), (1,2), (2,1)\} \\
& R_3 = \{(1,1), (2,2), (3,3), (1,3), (3,1)\} \\
& R_4 = \{(1,1), (2,2), (3,3), (2,3), (3,2)\} \\
& R_5 = \{(1,1), (2,2), (3,3), (1,2), (2,1), (1,3), (3,1), (2,3), (3,2)\} \\[3ex]
& \therefore \text{No. of relations} = 5 \\[2ex]
& \boxed{\text{Ans. (C)}}
\end{aligned}
$

Was this solution helpful?
YesNo