subforum will help you with the code.
[TEX]\exists t\in W_1\setminus W_2~\&~ \exists s\in W_2\setminus W_1[/TEX] gives
If you click on the “go advanced tab” you should see on the tool-bar. That gives the [TEX]..[/TEX] wrap. Your LaTeX code goes between them.
For proof by contradiction, make the above assumption.
If is a subspace, then