Finding a Set from its Intersection and Relative Complement | Set Theory

If we are given A intersect B, A-B, and B-A, can we determine what A and B are? We'll be going over this problem in today's set theory lesson with an example that will demonstrate the reasoning necessary to solve this problem!

In general, for two sets A and B, A is equal to (A intersect B) U (A - B) because (A intersect B) gives us the elements of A that are also in B, and (A - B) gives us the elements of A that are not in B. Similarly, B is equal to (A intersect B) U (B - A).

Note the use of "relative complement" in the title of this video; because A - B is the complement of B relative to A (as in, the set of all elements that are not in B, but are in A).

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