Question

Let A = {1, 2, 3}, B = {4, 5, 6, 7} and let f = {(1, 4), (2, 5), (3, 7)} be function from A to B, then f is

• A. one one
• B. many one
• C. one one onto
• D. None of these

Answer 1

Answer: (A)

one one

Answer 2

The function f: A → B is defined by f(1)=4, f(2)=5, f(3)=7.

1. One-one check: Distinct elements in A (1, 2, 3) map to distinct elements in B (4, 5, 7). Thus, f is one-one.
2. Onto check: The range of f is {4, 5, 7}. The codomain B is {4, 5, 6, 7}. Since the range is not equal to the codomain (element 6 in B has no pre-image), f is not onto.

Therefore, the function is one-one.