Question

The maximum number of equivalence relations on the set {4, 5, 6} containing (4,5) and (5,4) ?​

Answer 1

Answer:

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)}

These are the 5 relations on A which are equivalence