Question

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

• A. one-one
• B. onto
• C. many-one
• D. bijective

Answer 1

Answer: (A)

Given that, $A=\{1,2,3\}$ and $B=\{4,5,6,7\}$
Now, $f:A\to B$ is defined as $f=\{(1,4),(2,5),(3,6)\}$
Therefore, $f(1)=4,f(2)=5,f(3)=6$
It can be seen that the images of distinct elements of $A$ under $f$ are distinct.
Hence, function $f$ is one-one. But, $f$ is not onto, as $7\in B$ does not have a preimage in $A$.