Question

(v) Write an equivalence relation definie on a set {a,b,c,d)​

Answer 1

Answer:

The smallest equivalence relation is the identity relation R

1

={(a,a),(b,b),(c,c)}

Then two ordered pairs of two distinct elements can be added to give three more equivalence relations.

R

2

={(a,a),(b,b),(c,c),(a,b),(b,a)}

Similarly R

3

and R

4

can be made by taking (b,c),(c,b) and (a,c),(c,a) respectively.

Finally the largest equivalence relation i.e., the universal relation

R

5

={(a,a),(b,b),(c,c),(a,b),(b,a),(a,c),(c,a),(b,c),(c,b)}

Hence, total 5 equivalence relations can be