Answer
Let\[p\]be all electricity is off.
Let\[q\]be no lights work.
The form of the premises is
\[\begin{align}
& \underline{\begin{align}
& p\to q \\
& \tilde{\ }q \\
\end{align}}\ \ \ \ \ \underline{\begin{array}{*{35}{l}}
\text{If all electricity is off, then no lights work}\text{.} \\
\text{Some lights work}\text{.} \\
\end{array}} \\
& \ \therefore \ ?\ \ \ \ \ \ \ \ \ \ \ \text{Therefore, } \\
\end{align}\]
The conclusion \[\sim p\] is valid because it forms the contrapositive reasoning of a valid argument when it follows the given premises. The conclusion can be translated as some electricity is not off.Therefore, the valid conclusion from the provided premises is some electricity is not off.
