Question

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

A. 1
B. 2
C. 3
D. 5

Answer 1

D. 5

A = {1, 2, 3}

Then the equivalence relations would be,

P = {(1, 1), (2, 2), (3, 3)}

Q = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}

R = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}

S = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 1)}

T = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1, 3), (3, 1), (2, 3), (3, 1)}

Hence, total 5 equivalence relations.