Question

Let $A=\left\{1,2,3\right\}$ and $B=\left\{2,3,4\right\}$, then which of the following relations is a function from $A$ to $B$

• A. $\left\{(1,2),(2,3),(3,4),(2,2)\right\}$
• B. $\left\{(1,2),(2,3),(1,3)\right\}$
• C. $\left\{(1,3),(2,3),(3,3)\right\}$
• D. $\left\{(1,1),(2,3),(3,4)\right\}$

Answer 1

The correct option is C

$\left\{(1,3),(2,3),(3,3)\right\}$

Explanation for correct option:

Option C: $\left\{(1,3),(2,3),(3,3)\right\}$

In functions from $A$ to $B$, if we consider the ordered pair $\left(x,y\right)$, then the first element should belong to $A$ and second element should belong to $B$.

Also the function is defined from $A$ to $B$ if each element of set $A$ has a unique image in set $B$.

So if we see the option C, then the first elements of ordered pair belong to set $A$ and second element belong to set $B$. Also each element of set $A$ has unique image in set $B$.

Therefore the given relation is a function.

Explanation for incorrect options:

Option A: $\left\{(1,2),(2,3),(3,4),(2,2)\right\}$

Here, the element $2$ from set $A$ does not have a unique image in set $B$, therefore this is not a function.

Option B: $\left\{(1,2),(2,3),(1,3)\right\}$

Here also the element $1$from set $A$ does not have a unique image in set $B$, therefore this is not a function.

Option D: $\left\{(1,1),(2,3),(3,4)\right\}$

Here the second element of first ordered pair $\left(1,1\right)$ is not in set $B$, Hence this is not a relation as well as function.

Hence, option C is the correct answer.