READING:     I     §2     4                    Back to reading:     I     §2     3
begin quote ita"
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.
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Please read these notes from the beginning to here, and then paragraph 7 of §2.

DIFFERENCE OF SETS

I would like to do a proof of the equation at the end of the paragraph. Following the pattern of the previous section, we must prove the bottom line below, and then the upward direction of the vertical arrow establishes the desired result:

 =

The right pointing double arrow: If   x   is in the set on the left, then it is in   X   and it is not in   Y.   By the definition of the intersection of two sets, this means that   x   is in the set on the right.

The left pointing double arrow: If   x   is in the set on the right, then it is in   X   and it is not in   Y.   By the definition of the difference of two sets, this means that   x   is in the set on the left.

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