Question

A function f from the set of natural numbers to integers defined by f(n)=$\{\begin{array}{cc}\frac{n-1}{2},& \text{where n is odd}\\ -\frac{n}{2},& \text{where n is even}\end{array}$ is

• A. One-one but not onto
• B. Onto but not one-one
• C. One-one and onto both
• D. Neither one-one nor onto

Answer 1

The correct option is C One-one and onto both

$f:N\to I$

f(1) = 0, f(2) = -1, f(3) = 1, f(4) = -2, f(5) = 2\)

and f(6) = -3 so on.

In this type of function every elements of set A has unique image in set B and there is no elements left in set B. Hence f is one - one and onto function.