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Maximum Equivalence Relations on {1,2,3} | JEE Relations

JEE Maths question with a full step-by-step solution.

Question
The maximum number of equivalence relations on the set A={1,2,3}A = \{1, 2, 3\} is:
A11
B22
C33
D55correct
Solution
Each equivalence relation corresponds to a partition of AA. The partitions of {1,2,3}\{1, 2, 3\} are:
{1,2,3};\{1, 2, 3\};
{1,2}{3},{1,3}{2},{2,3}{1};\{1, 2\}\{3\}, \quad \{1, 3\}\{2\}, \quad \{2, 3\}\{1\};
{1}{2}{3}.\{1\}\{2\}\{3\}.
∴number of equivalence relations=1+3+1=5.\therefore \text{number of equivalence relations} = 1 + 3 + 1 = 5.
 Correct answer: (4)
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