# Is the set {(1, 4), (2, 5), (3, 5), (4, 6), (5, 7)} a function?

##### 1 Answer
Jul 4, 2015

Yes, it is a function.

#### Explanation:

A set of ordered pairs (a relation) is a function if and only if there are not two pairs with the same first element and different second elements.

Since no two pairs in this set have the same first element, there cannot be pairs with the same first and different second elements.

Note
Two more examples:

$\left\{\begin{matrix}- 1 & 4 \\ 2 & 7 \\ 0 & 1 \\ 6 & 2 \\ 5 & 7 \\ 0 & 1\end{matrix}\right\}$ is a function. (Writing $\left(0 , 1\right)$ twice has no effect on it being in the set.)

$\left\{\begin{matrix}3 & 1 \\ - 2 & 4 \\ 0 & 3 \\ 3 & 6 \\ 5 & - 4\end{matrix}\right\}$ is not a function. (The pairs $\left(3 , 1\right)$ and $\left(3 , 6\right)$ are both in the set, so it is not a function.