Let \(A = \{1, 2, 3\}\) and \(R = \{(1, 2), (2, 3)\}\). The minimum number of ordered pairs that must be added to R so that it becomes an equivalence relation on A is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 7
In an equivalence relation, related elements fall in the same class, and every element of a class is related to every element of that class.
Since 1 is related to 2 and 2 is related to 3, all three elements must be in one class. So the smallest equivalence relation containing R is
\(A \times A\), which has \(3 \times 3 = 9\) pairs
R already has 2 of them, so the number of pairs to be added is
\(9 - 2 = 7\)
They are (1, 1), (2, 2), (3, 3), (2, 1), (3, 2), (1, 3) and (3, 1).