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

Let us recall the formula n(A∪B)=n(A)+n(B)−n(A⋂B)It is given that n(∪)=100, n(B′)=30Thus n(B)=n(∪)−n(B′)=100−30=70Hence we obtain n(A⋂B)=n(A)+n(B)−n(A∪B)=60+70−75=55

Step by step solution to "Let A and B be subsets of U..."

High School
Algebra
Pre-Algebra
Equations, expressions, and inequalitie

Mylo O'Moore

Answered question

2021-05-31

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

Answer & Explanation

unessodopunsep

Skilled2021-06-01Added 105 answers

Let us recall the formula $n (A \cup B) = n (A) + n (B) - n (A ⋂ B)$
It is given that $n (\cup) = 100, n (B^{'}) = 30$
Thus $n (B) = n (\cup) - n (B^{'}) = 100 - 30 = 70$
Hence we obtain $n (A ⋂ B) = n (A) + n (B) - n (A \cup B)$

$= 60 + 70 - 75 = 55$

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