Which of the following is true on the basis of above diagram?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → ‘f’ is not a function from A → B
A rule f from A to B is a function only if every element of A has exactly one image in B.
In the diagram, two arrows leave a: one to 1 and one to 3. So a has two images, and f is not a function from A to B.
Why the other options are incorrect
Option (1) ‘f’ is a function from A → B — Incorrect. The element a has two images, 1 and 3.
Option (2) ‘f’ is one-one function from A → B — Incorrect. One-one is a property of functions only, and f is not a function.
Option (3) ‘f’ is onto function from A → B — Incorrect. All of 1, 2, 3, 4 are reached, but onto too is a property of functions only.