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  4. If the set A contains 5 elements and the set B contains 6 elements, then the number of one-one and onto mappings from A to B is

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Q. If the set $A$ contains $5$ elements and the set $B$ contains $6$ elements, then the number of one-one and onto mappings from $A$ to $B$ is

Relations and Functions - Part 2

Solution:

As A contains $5$ elements.
$\therefore $ For any one-one onto mapping $f$ : $A \to B$, $f (A)$ also contains $5$ elements but $B$ contains $6$ elements.
$\therefore f (A) \ne B$.
So, no one-one mapping from $A$ to $B$ can be onto.