Help with symbols

Question

I was wondering if I could get help with symbolically writing the English sentence, "There exists nothing outside of us."

The context I guess would be "the union of us", "us" could also be X and Y.

So I'm thinking backwards "E" with a strike through, [convey outside] {X U Y}.

But this says There doesn't exist .... the union of X and Y.

Any ideas?

Answer 1

If you use $X \cup Y$ to mean ”us”. You could say the complement of $X \cup Y$ is empty, which is logically equivalent to saying there is nothing ”outside” of us. In symbols this is $$(X\cup Y)^C = \emptyset$$