So We need to show that our topology is power set of $X$. how can I proceed?
closed as off-topic by Arnaud Mortier, Shailesh, Feng Shao, The Count, 0XLR Aug 18 at 0:19
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The cofinite topology on $X$ consists of the empty set and all cofinite sets, meaning all sets with finite complement. Since every subset of $X$ is finite, so is their complement. Therefore, the cofinite topology is equal to the power set.
Given any set $X$, we can define a topology $\tau$ on it, called the cofinite topology, by declaring the empty set $\phi$ and all the cofinite (look here for the definition of cofinite subset) subsets of $X$ to be the open sets (why is this collection form a topology on $X$?).
Now if $X$ is finite then the complement of any subset of $X$ is open in $\tau$ (why?).