Explanation:

To understand why the correct answer is option 'B', let's break down the problem and consider the properties of equivalence relations.

Equivalence Relations:
An equivalence relation on a set A satisfies three properties:
1. Reflexivity: Every element of A is related to itself.
2. Symmetry: If a is related to b, then b is also related to a.
3. Transitivity: If a is related to b and b is related to c, then a is related to c.

Number of Ordered Pairs:
Given that R is an equivalence relation on a finite set A with n elements, we need to determine the number of ordered pairs in R.

To count the number of ordered pairs, we can consider each element of A and count how many other elements it is related to. Since R is an equivalence relation, every element is related to itself, so we start with n ordered pairs.

For each element a in A, we need to count how many other elements it is related to. Let's denote this count as deg(a).

Since R is reflexive, deg(a) includes a itself.

For each pair of distinct elements a and b, if a is related to b, then b is related to a (symmetry property of equivalence relations). This means that if a is related to b, deg(a) includes b, and deg(b) includes a.

To count the number of ordered pairs, we sum up the values of deg(a) for each element a in A. However, we must be careful not to count any element twice.

Counting the Ordered Pairs:
Let's consider an element a in A.
- If a is related to itself, deg(a) includes a.
- If a is related to b (b is distinct from a), deg(a) includes b, and deg(b) includes a.

Therefore, deg(a) includes a and all the distinct elements b that are related to a.

Since there are n elements in A, we have to find deg(a) for each element a.
- If deg(a) = 1, it means a is related only to itself.
- If deg(a) = 2, it means a is related to one other element.
- If deg(a) = 3, it means a is related to two other elements.
- And so on...

The maximum value of deg(a) is n, which occurs when every element is related to every other element in A. In this case, the number of ordered pairs is n.

Conclusion:
Given that the number of ordered pairs in R is at least n when every element is related to every other element, the correct answer is option 'B' - greater than or equal to n.