Sets, Relations & Functions
Counting One-One Functions from Lattice Set
nta_pyq_2024_apr
Grade 11
Question:
Let $A=\{(x,y):2x+3y=23,\ x,y\in\mathbb{N}\}$ and $B=\{x:(x,y)\in A\}$. Then the number of one-one functions from $A$ to $B$ is equal to ________.
Step-by-Step Solution
Key Concept: Natural number solutions of $2x+3y=23$: $(1,7),(4,5),(7,3),(10,1)$. $|A|=4$. $B=\{1,4,7,10\}$, $|B|=4$.
$|A|=|B|=4$. One-one functions $=4!=24$.
Correct Answer: 24