Question

On a set {a,b,c}, we define an equivalence relation 'R'. If this relation is {(a,a),(b,b),(c,c),(a,b),(b,a)}. How many equivalence classes will be formed from this relation?

• A. 1
• B. 0
• C. 2
• D. 3

Answer 1

The correct option is C

2

To find the equivalence class, we will first all the elements from the equivalence class of that element. To do this, we just have to list down all the elements related to that element because it will be related all the elements of the equivalence class from which it is.

Let's take 'a' first. In the given relation 'a' is related a and b through the relations (a,a), (a,b) and (b,a). So the equivalence class of a is {a,b}. Now we have only one element left from the set, c. So it will be the second equivalent class.