Question

If relation R is defined as "Is of the same color" on set of objects. Then the total number of equivalence classes on the set with respect to R is equal to.

• A. Number of distinct objects in the set.
• B. Number of distinct colors in the set
• C. (Number of objects)${}^2$
• D. (Number of distinct colors)${}^2$

Answer 1

The correct option is B

Number of distinct colors in the set

Each of the given sets will be an equivalence class because,

1. All the objects of a color will be related to all object of that color
2. There won't be any relation between objects of different colors
3. The union of all the colors will give the on which we defined the relation
4. There won't be any common objects between any two different colors

So we can say that there will be as many equivalence classes as the number of colors