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

1.	The maximum number of equivalence relations on the set A = {1, 2, 3} are(A) 1 (B) 2(C) 3 (D) 5
Answer» (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’.

The maximum number of equivalence relations on the set A = {1, 2, 3} are(A) 1 (B) 2(C) 3 (D) 5

Answer»

(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’.