Originally Posted by

**FernandoRevilla** If you have already studied the concept of universal set $\displaystyle U$ , the complementary $\displaystyle M^c$ of a subset $\displaystyle M\subset U$, distributive and Morgan's laws, etc you can prove the equality in another way.

Choosing as universal set any set $\displaystyle U$ such that $\displaystyle S\cup T\subset U$ (in this case for example $\displaystyle U=T$) we have $\displaystyle M-N=M\cap N^c$ for $\displaystyle M,N\subset U$ . So,

$\displaystyle T-(T-S)=T\cap (T-S)^c=T\cap (T\cap S^c)^c=T\cap (T^c\cup S)=$

$\displaystyle (T\cap T^c)\cup(T\cap S)=\emptyset \cup (T\cap S)=T\cap S=S$