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Q.
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
Relations and Functions - Part 2
Solution:
Given that, $A=\{1,2,3\}$ and $B=\{4,5,6,7\}$
Now, $f: A \rightarrow B$ 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 $A$.