CMI Data Science 2025 | Part A | Question: 1

Question

Let $X=\{1,2,3\}$ and $Y=\{a, b, c, d\}$ be two finite sets. Which of the following statements regarding functions from $X \rightarrow Y$ is/are true?

• A. The number of one-to-one functions is $3^{4}$.
• B. There are as many one-to-one functions as onto functions.
• C. The number of onto functions is strictly less than the number of one-to-one functions.
• D. The number of one-to-one functions is $24.$

Answer 1

Let's Go  with the options 

$A)$ No of  one-one funtions will be  $4p3=24$ 

$B)$  No of onto functions will be $0$ bcz $|Y| >|X|$ which is not same as one one functions

$C)$ this is true From option $B$ & $A$

$D)$ This is true .

So $C$ & $D$ are answer