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
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