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CHAPTER I [:] Notions from Set Theory [...] 2. OPERATIONS ON SETS. "end quote
These pages assume that the reader has the book and is reading along.    
topic index     contents
Please read these notes from the beginning to here, and then the third paragraph of 2.

COMPLEMENT OF A SET

For emphasis and an example, I would like to quote Rosenlicht's definition of the complement of a set.

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If   X   is a subset of a set   S,   then the complement of   X   in   S   is the set of all elements of   S   which are not elements of   X   [...]

That is   .

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Example: Let   S   be all the matter and energy in our solar system - out to just beyond that space craft that is escaping. Let   X   be the union of all of 'our' economies that exist within the solar system. Let   M   be the part of   X   that exists as matter (mass), and let   E   be the part of   X   that exists as energy. Then the intersection of   M   and   E   is the empty set, the union of   M   and   E   is   X,   and the complement of   X   in   S   is not the empty set.

on to reading 2