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I need to prove:

  1. $\bigcup\limits_{i} A - \bigcup\limits_j B \subset \bigcup\limits_j (A-B)$
  2. $\bigcap\limits_{i} A - \bigcap\limits_j B \subset \bigcup\limits_j (A-B)$

So when can the equality hold?

Appreciate your help.

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    You can use $\TeX$ on this site by enclosing formulas in dollar signs; single dollar signs for inline formulas and double dollar signs for displayed equations. You can see the source code for any math formatting you see on this site by right-clicking on it and selecting "Show Math As:TeX Commands". [Here](http://meta.math.stackexchange.com/questions/5020/mathjax-basic-tutorial-and-quick-reference)'s a basic tutorial and quick reference. In the present case, the commands you need are `\cup` for $\cup$, `\cap` for $\cap$ and `\subset` for $\subset$. There's an "edit" link under the question.2012-09-15

3 Answers 3