Question

The maximum number of equivalence relations on the set A= { 1, 2, 3} are

• A. 1
• B. 2
• C. 4
• D. 5

Answer 1

The correct option is D 5

Given that, A= {1, 2, 3}. Now, the possible equivalence relations are as follows:
R₁ = {(1, 1), (2, 2), (3, 3)}
R₂= {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}
R₃ = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}
R₄= ((1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}
R₅ = {(1,1), (2,2) , (3,3) , (1,2), (1,3),(2,1),(2,3) (3,1),(3,2)}
Maximum number of equivalence relation is '5'.