Question

Let A and B be subsets of U with n(U)=100,n(A)=60,n(B′)=30,n(U)=100,n(A)=60,n(B ′ )=30, and n(A U B) = 75, Find n(A ⋂ B)

Equation, expression, and inequalitie
ANSWERED
asked 2021-05-31
Let A and B be subsets of U with n(U)=100,n(A)=60,n(B′)=30,n(U)=100,n(A)=60,n(B ′ )=30, and n(A U B) = 75, Find \(\displaystyle{n}{\left({A}⋂{B}\right)}\)

Expert Answers (1)

2021-06-01
Let us recall the formula \(\displaystyle{n}{\left({A}{U}{B}\right)}={n}{\left({A}\right)}+{n}{\left({B}\right)}-{n}{\left({A}⋂{B}\right)}\)
It is given that n(U)=100, n(B')=30
Thus n(B)=n(U)-n(B')=100-30=70
Hence we obtain \(\displaystyle{n}{\left({A}⋂{B}\right)}={n}{\left({A}\right)}+{n}{\left({B}\right)}-{n}{\left({A}{U}{B}\right)}\) =60+70-75 =55
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