Explanation:

To make a relation R an equivalence relation, we need to check if it satisfies three conditions: reflexivity, symmetry, and transitivity.

Reflexivity:
A relation is reflexive if every element is related to itself. In other words, for every element 'a' in the set, (a, a) should be in the relation. In this case, the set is {1, 2, 3}, and (1, 1) and (2, 2) are not given in the relation R. So, we need to add these two pairs to make R reflexive.

Symmetry:
A relation is symmetric if for every pair (a, b) in the relation, the pair (b, a) is also in the relation. In this case, (1, 2) is given in the relation R, but (2, 1) is not. So, we need to add (2, 1) to make R symmetric.

Transitivity:
A relation is transitive if for every three pairs (a, b), (b, c), and (a, c) in the relation, the pair (a, c) is also in the relation. In this case, (1, 2) and (2, 3) are given in the relation R. To check transitivity, we need to check if (1, 3) is in the relation R. Since it is not given, we need to add (1, 3) to make R transitive.

Adding Ordered Pairs:
To make R reflexive, we need to add (1, 1) and (2, 2).
To make R symmetric, we need to add (2, 1).
To make R transitive, we need to add (1, 3).

So far, we have added 5 ordered pairs to R. Now, let's check the updated relation:

R = {(1, 2), (2, 3), (1, 1), (2, 2), (2, 1), (1, 3)}

Checking Equivalence:
Now, let's check if R satisfies reflexivity, symmetry, and transitivity.

Reflexivity: (1, 1), (2, 2), and (3, 3) are in the relation R. So, R is reflexive.

Symmetry: (1, 2) and (2, 1) are in the relation R. So, R is symmetric.

Transitivity: (1, 2), (2, 3), and (1, 3) are in the relation R. So, R is transitive.

Since R satisfies all three conditions, it is now an equivalence relation.

Therefore, the minimum number of ordered pairs that need to be added to R to make it an equivalence relation is 5.

Answer: Option D) 7