Let A and B be finite sets with \(n(B) = 4\), and let \(f : A \to B\) be a function that is onto but not one-one. Then \(n(A)\) can be
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 5
Since f is onto, each of the 4 elements of B is the image of at least one element of A. So
\(n(A) \ge 4\)
If \(n(A) = 4\), the 4 elements of A cover the 4 elements of B, one each, so different elements have different images and f would be one-one.
Since f is not one-one, A must have more than 4 elements:
\(n(A) \ge 5\)
Among the options, only \(n(A) = 5\) is possible.