Let $A=\{(x, y): 2 x+3 y=23, x, y \in \mathbb{N}\}$ and $B=\{x:(x, y) \in A\}$. Then the number of one-one functions from $A$ to $B$ is equal to _________.
Answer (integer)
24
Solution
<p>$$\begin{aligned}
& A=\{(x, y) ; 2 x+3 y=23, x, y \in N\} \\
& A=\{(1,7),(4,5),(7,3),(10,1)\} \\
& B=\{x:(x, y) \in A\} \\
& B=\{1,4,7,10\}
\end{aligned}$$</p>
<p>So, total number of one-one functions from A to B is $4!=24$</p>
About this question
Subject: Mathematics · Chapter: Sets, Relations and Functions · Topic: Sets and Operations
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