Sets, Relations & Functions
Equivalence Relations / Bell Numbers
nta_pyq_2025_apr
Grade 11
The number of non-empty equivalence relations on the set $\{1, 2, 3\}$ is:
Step-by-Step Solution
Key Concept: The number of equivalence relations on a set of $n$ elements equals the Bell number $B(n)$. For $n=3$, $B(3)=5$.
Equivalence relations correspond to partitions. Partitions of $\{1,2,3\}$: $\{\{1\},\{2\},\{3\}\}$, $\{\{1,2\},\{3\}\}$, $\{\{1,3\},\{2\}\}$, $\{\{2,3\},\{1\}\}$, $\{\{1,2,3\}\}$ — total 5. $B(3) = 5$.
Correct Answer: 5