Question

Let $A=(1,2,3)$ and $B=(a,b,c)$. If $f$ is a function from $A$ to $B$ and $g$ is a one-one function from $A$ to $B$, then the maximum number of definitions of.

• A. $f$ is $9$
• B. $g$ is $9$
• C. $f$ is $27$
• D. $g$ is $6$

Answer 1

Answer: (C), (D)

The correct options are
C $f$ is $27$
D $g$ is $6$

From a set of $n$ elements to a set of $m$ elements

Total number of functions $={\left(m\right)}^n$

$f$ is a function from $A$ to $B$

So, total number of functions $=3^3=27$.

Total number of one one functions $=m(m-1)(m-2)......(m-(n-1\left)\right)$

Total one one functions $=3\times \times 2\times 1=6$

So, options C and D are correct.