SOLUTION: Given that E and F are sets and n(E\F)=12 and n(F\E)=30, what is the smallest possible value for n(EUF)

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Question 1026954: Given that E and F are sets and n(E\F)=12 and n(F\E)=30, what is the smallest possible value for n(EUF)
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Since E∪F = (E-F)∪(E∩F)∪(F-E), and each of the three components are mutually exclusive, it follows that.
n(E∪F) = n(E-F) + n(E∩F) + n(F-E) = 12 + n(E∩F) + 30 = 42 + n(E∩F)
==> n(E∪F) = 42 + n(E∩F) ≥ 42.
n(E∪F) = 42 only when E∩F = ∅.