Question:
The maximum number of equivalence relations on the set A = {1, 2, 3} are
(A) 1
(B) 2
(C) 3
(D) 5
Solution:
(D) 5
Given, set A = {1, 2, 3}
Now, the number of equivalence relations 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, 2, 3) ⇔ A x A = A2}
Thus, maximum number of equivalence relation is ‘5’.
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