This

subforum will help you with the code.

[TEX]\exists t\in W_1\setminnus W_2~\&~ \exists s\in W_2\setminnus W_1[/TEX] gives $\displaystyle \exists t\in W_1\setminnus W_2~\&~ \exists s\in W_2\setminnus W_1 $

If you click on the “go advanced tab” you should see $\displaystyle \boxed{\Sigma} $ 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 $\displaystyle W_1\cup W_2$is a subspace, then $\displaystyle s+t\in W_1\cup W_2~.$

Now what?