10. Prove $A \cup B = (A \cap B) \cup (A \setminus B) \cup (B \setminus A)$.
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Suppose x is an element of (AnB) U (A B) U (B | A). Then, x is either in AnB, A B, or B | A. If x is in AnB, then x is in both A and B. Therefore, x is in AU B. If x is in A B, then x is in either A or B (or both). Therefore, x is in AU B. If x is in B | Show more…
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