I have a problem I need to do, and I was wondering what the method is to convert set notation to set builder notation. The problem is:

Show that if A, B, and C are sets than

A $\displaystyle \cup$ B $\displaystyle \cup$ C = A + B + C - (A $\displaystyle \cap$ B) - (A $\displaystyle \cap$ C) - (B $\displaystyle \cap$ C) + (A $\displaystyle \cap$ B $\displaystyle \cap$ C)

If there is a better method than converting to set builder notation, let me know what it is (Although I would still like to know a general method from converting from this notation to a set builder notation).

Thanks,

James