Let \(A = \{1, 2, 3, \ldots, 10\}\) and let R be the equivalence relation on A given by \(R = \{(a, b) : a - b \text{ is divisible by } 4\}\). The equivalence class [2] is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → {2, 6, 10}
The equivalence class [2] is the set of all elements b of A with \((2, b) \in R\), that is, with \(b - 2\) divisible by 4.
\(b - 2 = 0, 4, 8\)
\(b = 2, 6, 10\)
The next value, \(b = 14\), is not in A. So \([2] = \{2, 6, 10\}\). Note that 2 itself belongs to its own class.