The maximum number of equivalence
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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