Let R be an equivalence relation on a finite set A having n elements. Then, the number of ordered pairs in R is

The correct option is Greater than or equal to n.

Let us understand why this is the correct answer step-by-step.

Step 1: Understand the definition of an equivalence relation
Let $A$ be a finite set containing $n$ elements, which we can represent as:
$A=\{a_1,a_2,\dots ,a_n\}$

An equivalence relation $R$ on set $A$ is a binary relation that satisfies three fundamental properties:
1. Reflexivity: For every element $a\in A$, the ordered pair $(a,a)$ must belong to $R$.
2. Symmetry: If $(a,b)\in R$, then $(b,a)\in R$.
3. Transitivity: If $(a,b)\in R$ and $(b,c)\in R$, then $(a,c)\in R$.

Step 2: Apply the property of Reflexivity
Since $R$ is an equivalence relation, it must be reflexive. This means that for each of the $n$ elements in the set $A$, the relation $R$ must contain the ordered pair representing that element's relation to itself.
Therefore, the relation $R$ must contain at least the following ordered pairs:
$(a_1,a_1),(a_2,a_2),\dots ,(a_n,a_n)$

Step 3: Determine the minimum number of ordered pairs
The list of reflexive pairs shown in Step 2 consists of exactly $n$ distinct ordered pairs. Because these pairs must be present in $R$ for it to be reflexive, the number of elements (ordered pairs) in $R$, denoted as $\left|R\right|$, cannot be less than $n$.
Thus, we have:
$\left|R\right|\ge n$

Depending on the specific equivalence relation, there may be additional ordered pairs present in $R$ (for instance, the universal relation on set $A$ contains $n^2$ ordered pairs). Consequently, the total number of ordered pairs in $R$ is always greater than or equal to $n$.