Let \(A = \{1, 2, 3, \ldots, 50\}\) and let R be the equivalence relation on A given by \(R = \{(a, b) : \text{the sum of the digits of } a \text{ is equal to the sum of the digits of } b\}\). The number of elements in the equivalence class [13] is
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 5
The equivalence class [13] is the set of all elements of A related to 13.
The sum of the digits of 13 is
\(1 + 3 = 4\)
So [13] contains every number from 1 to 50 whose digits add up to 4:
one-digit: 4
two-digit: 13, 22, 31, 40
\([13] = \{4, 13, 22, 31, 40\}\)
So [13] has 5 elements. (The single-digit number 4 is easy to miss.)