Sets, Relations & Functions
Multiplicative Functions / Counting
nta_pyq_2023_jan
Grade 11
Question:
Let $A = \{1, 2, 3, 5, 8, 9\}$. Then the number of possible functions $f: A \to A$ such that $f(m \cdot n) = f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to ______.
Step-by-Step Solution
Key Concept: Use the multiplicative constraint: $f(1)=1$, $f(9)=f(3)^2$; enumerate valid assignments for each element.
Carefully enumerating valid assignments satisfying all product constraints gives 432.
Correct Answer: 432