Assertion (A): If set A contains 7 elements and set B contains 6 … - Vidyadip

Question

Assertion $(A):$ If set $A$ contains $7$ elements and set $B$ contains $6$ elements, then the number of one$-$one onto mapping from $A$ to $B$ is $420 $.
Reason $(R):$ If $A$ and $B$ are two non$-$empty sets containing $m$ and $n$ elements respectively, then number of one$-$one onto functions from $A$ to $B =\left\{\begin{array}{l}n !, \text { if } m=n \\0, \text { if } m \neq n\end{array}\right. \text {. }$

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Answer

Clearly, reason is true.
Now, $m=7$ and $n=6$ i.e., $m \neq n$
$\therefore$ Number of one$-$one onto mapping from $A$ to $B$ is $0$ .
$\therefore$ Assertion is false and Reason is true.

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