The maximum number of equivalence relations can be defined on the set A= 1,2,3 are

Question

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

Tardigrade Admin · Accepted Answer

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= (1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(3,1),(2,3),(3,2)

Q. The maximum number of equivalence relations can be defined on the set $A = {1, 2, 3}$ are

1

2

3

5

$R_{1} = {(1, 1), (2, 2), (3, 3)}$
$R_{2} = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}$
$R_{3} = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}$
$R_{4} = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}$
$R_{5} = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1, 3), (3, 1), (2, 3), (3, 2)}$

Q. The maximum number of equivalence relations can be defined on the set A={1,2,3} are

1

2

3

5

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

Q. The maximum number of equivalence relations can be defined on the set $A = {1, 2, 3}$ are

$R_{1} = {(1, 1), (2, 2), (3, 3)}$
$R_{2} = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}$
$R_{3} = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}$
$R_{4} = {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}$
$R_{5} = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1, 3), (3, 1), (2, 3), (3, 2)}$