Relations

Question

The minimum number of ordered pairs that must be added to the relation R = {(1, 2), (2, 3)} on the set A = {1, 2, 3} to make it an equivalence relation is

RankGuru · Accepted Answer

1. **Reflexive Closure**: Add $(1,1), (2,2), (3,3)$ [3 pairs].
2. **Symmetric Closure**: Add $(2,1), (3,2)$ [2 pairs].
3. **Transitive Closure**: 
   - Since we have $(1,2)$ and $(2,3)$, we must add $(1,3)$.
   - By symmetry, once we add $(1,3)$, we must add $(3,1)$. [2 pairs].
4. **Verify**: The resulting relation is $\{(1,1), (2,2), (3,3), (1,2), (2,1), (2,3), (3,2), (1,3), (3,1)\}$, which is $A 	imes A$ (the largest equivalence relation).
5. **Total Added**: $3 + 2 + 2 = 7$.

Rank Guru

Relations

Select the correct option:

Solution

🔒 Solution Hidden from View

More relations Practice Questions

For two positive numbers a and b, which of the following is always true?

Let R be a relation on the set N of natural numbers defined by nRm \u21Longleftrightarrow n is a fac...

If R is a relation from a finite set A having m elements to a finite set B having n elements, then t...

If A = {a, b, c}, then the number of equivalence relations on A containing (a, b) is

The relation 'less than' on the set of real numbers R is

About This Question

Solution