Answer
Use letters to represent each simple statement in the argument.
p: We close the door.
q: There is less noise.
Express the premises and conclusion symbolically as:
\[\frac{\begin{align}
& p\to q \\
& q \\
\end{align}}{\therefore p}\ \ \ \ \ \ \frac{\begin{align}
& \text{If we close the door, then there is less noise}\text{.} \\
& \text{There is less noise}\text{.} \\
\end{align}}{\therefore \text{We closed the door}\text{.}}\]
The argument is in the form of Fallacy of the Converse.
So, the argument is invalid.
