If $n(U) = 50$, $n(A) = 30$, $n(B) = 25$, and $n(A \cup B) = 45$, find $n(A \cap B)$.
A5
B10CORRECT
C15
D20
GCEMathematicsSets and Logic2023
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Why the answer is B, and why the others tempt you.
Using the formula $n(A \cup B) = n(A) + n(B) - n(A \cap B)$, we get $45 = 30 + 25 - n(A \cap B)$. Solving gives $n(A \cap B) = 55 - 45 = 10$.
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