Consider the statement
For all sets A and B, (A ? B) ? B = ?.
The proof below is the beginning of a proof using the element method for proving that the set equals the empty set. Complete the proof without using any of the set properties from Theorem 6.2.2.
Proof: Suppose the given statement is false. Then there exist sets A and B such that (A ? B) ? B ?= ?. Thus there is an element x in (A ? B) ? B. By definition of intersection,. . . .
Proof: Suppose the given statement is false. Then there exist sets A and B such that (A ? B) ? B ?= ?.
Thus there is an element, say x, in (A ? B) ? B.
By definition of intersection, x ? A ? B and x ? B.
By definition of set difference (since x ? A ? B), x ? A and x /? B.
Hence x ? B and x /?
B, which is a contradiction.
[Arriving at this contradiction shows that the given statement is not false; so it is true that for
all sets A and B, (A ? B) ? B = ?.]
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A. 
B. 
C. 
D. 