Let A= 1,2,3,5,8,9 . Then the number of possible functions f: A arrow A such that f(m ⋅ n)=f(m) ⋅ f(n) for every m, n ∈ A with m ⋅ n ∈ A is equal to

Question

Let A= 1,2,3,5,8,9 . Then the number of possible functions f: A arrow A such that f(m ⋅ n)=f(m) ⋅ f(n) for every m, n ∈ A with m ⋅ n ∈ A is equal to (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

f(1)=1 ; f(9)=f(3) × f(3) i.e., f(3)=1 or 3 Total function =1 × 6 × 2 × 6 × 6 × 1=432

Q. 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______

$f (1) = 1; f (9) = f (3) \times f (3)$
i.e., $f (3) = 1$ or 3
Total function $= 1 \times 6 \times 2 \times 6 \times 6 \times 1 = 432$

Q. Let A={1,2,3,5,8,9}. Then the number of possible functions f:A→A such that f(m⋅n)=f(m)⋅f(n) for every m,n∈A with m⋅n∈A is equal to______

f(1)=1;f(9)=f(3)×f(3) i.e., f(3)=1 or 3 Total function =1×6×2×6×6×1=432

Q. 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______

$f (1) = 1; f (9) = f (3) \times f (3)$
i.e., $f (3) = 1$ or 3
Total function $= 1 \times 6 \times 2 \times 6 \times 6 \times 1 = 432$