## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

$n(A) = 50$
Given: $n(A∪B)= 60 , n(A∩B) = 40, n(A) = n(B)$ Use the formula $n(A \cup B) = n(A) + n(B) - n(A\cap B)$ to obtain: $n(A \cup B) = n(A) + n(B) - n(A\cap B) \\n(A \cup B) = n(A) + n(A) - n(A\cap B) \\n(A \cup B) = 2[n(A)] - n(A \cap B) \\60 = 2[n(A)] - 40 \\60+40=2[n(A)] \\100=2[n(A)] \\\frac{100}{2}=\frac{2[n(A)]}{2} \\50=n(A)$