Question

Let \( D = \{a, b, c\} \). How many distinct ways can \( D \) be partitioned into non-empty subsets, representing equivalence relations?

• A. 2
• B. 3
• C. 5
• D. 6

Hint:

For finding distinct partitions of a set, you can use the Bell number or directly list the partitions for small sets.

Answer 1

The Correct Option is B

The number of distinct partitions of a set \( D \) into non-empty subsets is equal to the number of equivalence relations on \( D \). 

For \( D = \{a, b, c\} \), the number of distinct partitions is 3. 

This corresponds to the partitions \( \{\{a\}, \{b, c\}\} \), \( \{\{a, b\}, \{c\}\} \), and \( \{\{a, b, c\}\} \).