Relations Question 18
Question: A function $f$ from the set of natural number to integers defined by
$f(n)=\begin{cases} \frac{n-1}{2} & \text { when } \mathrm{n} \text { is odd } \\ -\frac{n}{2} & \text { when } \mathrm{n} \text { is even } \end{cases}$
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:
$ 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 unique image in set B and there is no element left in set B. Here f is a one-one and onto function.
BETA
