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 $g$ is $6$
D $f$ is $27$

For g, 1 can be mapped to a, b or c. 2 can be mapped to any 2 of the remaining options while 3 can be only mapped to the remaining option.

Total no. of definitions = $3\times 2\times 1=6$

For g, 1 can be mapped to a, b or c. 2 can be mapped to a, b or c .3 can also be mapped to a,b or c.

Total no. of definitions = $3\times 3\times 3=27$