How to make an expression

Question

Please help to make an expression, with which you could get from the sets A, B, C a set D.

Answer 1

First of all, you must make it clear of the meaning of your 'expression'. Does it mean an expression involving only union and intersection?

A quick answer: $$\left ( A-\left ( B\cup C \right ) \right )\cup \left ( B-\left ( C\cup A \right ) \right ) \cup\left ( C-\left ( A\cup B\right ) \right ) \cup \left ( A\cap B\cap C \right ),$$or equivalently $$A\cup B\cup C -\left ( \left ( A\cap B \right )\cup \left ( B\cap C \right )\cup \left ( C\cap A \right ) - A\cap B\cap C \right )$$