The number of non-empty equivalence relations on the set $\{1, 2, 3\}$ is _____.
Step-by-Step Solution
Key Concept: Equivalence relations $\leftrightarrow$ partitions of $\{1, 2, 3\}$. Partitions: $\{\{1\}, \{2\}, \{3\}\}; \{\{1, 2\}, \{3\}\}; \{\{1, 3\}, \{2\}\}; \{\{2, 3\}, \{1\}\}; \{\{1, 2, 3\}\}$. Total = 5 (the Bell number $B_3 = 5$).
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Correct Answer: 5