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Let A + B = (A - B) U (B - A) also known as the symmetric difference.
1. Look for the identity and let e be the identity element
A + e = A
(A - e) U (e - A) = A
Now there are two cases:
1. (A - e) = A
This equation can be interpreted as removing from A all elements that belong to e to yield the set A. In order for this statement to be true, the identity element e must be the empty set.
2. (e - A) = A
This equation can be interpreted as removing from e all elements that belong to A to generate a set A. Is this statement undefined?
Let A + B = (A - B) U (B - A) also known as the symmetric difference.
1. Look for the identity and let e be the identity element
A + e = A
(A - e) U (e - A) = A
Now there are two cases:
1. (A - e) = A
This equation can be interpreted as removing from A all elements that belong to e to yield the set A. In order for this statement to be true, the identity element e must be the empty set.
2. (e - A) = A
This equation can be interpreted as removing from e all elements that belong to A to generate a set A. Is this statement undefined?
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