Sets Relations And Functions Question 41
A function f from the set of natural numbers to integers defined by $ f(n)= \begin{cases} \frac{n-1}{2},\text{when n odd} \\ -\frac{n}{2}, \text{when n is even} \\ \end{cases}$ is .
Options:
A) one-to-one but not onto.
B) onto but not one-one
C) one-to-one and onto both.
D) neither one-one nor onto.
Show Answer
Answer:
Correct Answer: C
Solution:
- [c] $ f:N\to I $ $ f( 1 )=0,f( 2 )=-1, $ $ f( 3 )=1,f( 4 )=-2, $ $ f( 5 )=2,f( 6 )=-3, $ and so on. In this function, every element of set A has a unique image in set B and there are no elements left in set B. Here f is a one-one and onto function.
BETA
