Let A=1,2,3,5,8,9.

Question

Let $A={1,2,3,5,8,9}$. Then the number of possible functions $f:A	o A$ 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 \_\_\_\_\_\_\_\_\_\_\_.

Answer: 432

Accepted Answer

$f(1.n)=f(1).f(n)\Rightarrow f(1)=1$.

$f(3.3)=(f(3){)}^{2}$

Hence, the possibilities for $(t(3),(9))$ are $(1,1)$ and $(3,9)$.

Other three i.e. $f(2),f(5),f(8)$

Can be chosen in 6${}^{3}$ ways.

Hence, total number of functions

${6}^{3}	imes 2=432$

Solutions · 1