# A little bit of set theory

• Nov 11th 2013, 07:13 AM
director
A little bit of set theory
I'm given an open set O, a closed set F, and an arbitrary set E;
where E is a subset of O and F is a subset of E.

Is it true that O~F = (E~F) union (O~E)?
• Nov 11th 2013, 08:08 AM
Plato
Re: A little bit of set theory
Quote:

Originally Posted by director
I'm given an open set O, a closed set F, and an arbitrary set E;
where E is a subset of O and F is a subset of E.
Is it true that O~F = (E~F) union (O~E)?

I assume that by $O\sim F$ that you mean set difference.

That is $O\setminus F=O\cap F^c$, if so then yes $O\setminus F=(E\setminus F)\cup(O\setminus E)$.

You should try to prove that.