Answer:
True.
Step-by-step explanation:
If a function is multiplicative then it hold following properties
1.f(1)=1
2.[tex]\f(a\cdot b)=f(a)\cdot f(b)[/tex] hold for all a and b when even a and b are not co-prime.
Let [tex]\sigma(n)[/tex] is a function of sum of divisor of n
[tex]\sigma (n)[/tex]=Sum of divisor of n
If n=1 then
[tex]\sigma (1)=1[/tex]
It is satisfied first property.
Suppose n=9
Then divisor of 9=1,3,9
Sum of divisor=1+3+9=13
Divisor of 3=1,3
Sum of divisors of 3=1+3=4
[tex]\sigma (9)=13[/tex]
[tex]\sigma (3)\cdot \sigma(3)=4\cdot 4=16[/tex]
Hence, [tex]\sigma (a\cdot b)\neq \sigma(a)\cdot \sigma(b)[/tex]
Therefore, [tex]\sigma(n)[/tex] is not a multiplicative function.
Hence, given statement is true.
