Set Theory and Equality Let $A$ and $X$ be sets. Show that $X\setminus(X\setminus A)\subseteq A$, and that equality holds if and only if $A\subseteq X$. 
I understand why this holds but am not sure how to 'show' this. Any advice would be appreciated. 

Start with the definition/alternate expression for "setminus": $A\setminus B=A\cap B^c$, where $B^c$ is the complement of $B$:
$$X\setminus(X\setminus A)=X\cap (X\cap A^c)^c = X\cap (X^c \cup A) = (X\cap X^c) \cup (X \cap A)= X\cap A$$
Does that help?
