I need to determine which of the following are true and prove it... if it is false then I have to give a counterexample.
If $A$ is a subset of a topological space, then $A' \subseteq A$
For any closed subset $A$ of a topological space, $A' \subseteq A$.
I think this theorem is helpful "Let $(X, \mathfrak T)$ be a topological space and let $A \subseteq X$. The set $A$ is closed iff $A' \subseteq A$.
$A'$ represents limit points my defintion for limit points is: Let $(X, \mathfrak T)$ be a topological space and let $A \subseteq X$. A point $x \in X$ is said to be a limit point of $A$ provided that every open set containing $x$ contains a point of $A$ different from $x$.
I think the first statement is true and the second statement is false.