Question

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

(A) 1 

(B) 2

(C) 3 

(D) 5

Answer 1

(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’.