This 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

Now what?