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 $6$

For every number in set $A$ there are $3$ choices in set $B$, Hence the total number of functions from $A\to B$ are $3\times 3\times 3=27$.
For the first number in set $A$ there are $3$ choices in set $B$,
Since the function is one-one the second number in set $A$ has only $2$ choices in set $B$ as we can not mapped the two number to the same element.
Similarly, the third number has only one choice.
Therefore the total number of one one functions from $A$ to $B$ are $3\times 2\times 1=6$