Let \(A = \{1, 2, 3, 4\}\) and \(B = \{p, q, r\}\), and let \(f : A o B\) be given by \(f = \{(1, q), (2, r), (3, p), (4, q)\}\). Then f is
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → onto but not one-one
From the pairs, the images are
\(f(1) = q\), \(f(2) = r\), \(f(3) = p\), \(f(4) = q\)
f is not one-one, since two different elements have the same image:
\(f(1) = f(4) = q\)
f is onto, since each of p, q and r is an image: p of 3, q of 1 and r of 2.
So f is onto but not one-one.