Find the value

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

Solution:

To state: Whether f is one-one

Given: $f=\{(1,4),(2,5),(3,6)\}$

Here the function is defined from $A \rightarrow B$

For a function to be one-one if the images of distinct elements of $A$ under $f$ are distinct i.e. 1,2 and 3 must have a distinct image.

From $f=\{(1,4),(2,5),(3,6)\}$ we can see that 1,2 and 3 have distinct image.

Therefore $\mathrm{f}$ is one-one

Ans) $f$ is one-one