Question

If n(A) = 33 , n(A ∪ B )= 45, n(B) = 20 then find n(A ∩ B)​

Answer 1

Answer:

If n(A) = 7, n (A ∪ B) = 11, and n(B) = 5, then what is n (A ∩ B)?

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17 Answers



Francis Xavier

, Business & Computing practioner at Makerere University Business School (2015-present)

Answered 3 years ago

Ifn(A)=7,n(A∪B)=11,andn(B)=5,thenwhatisn(A∩B)?Ifn(A)=7,n(A∪B)=11,andn(B)=5,thenwhatisn(A∩B)?

Solution

n(A)=7n(A)=7

n(B)=5n(B)=5

n(A∪B)=11n(A∪B)=11

(A∩B)=?(A∩B)=?

Let the intersection of A and B =n,n(Aonly)=7−n,n(Bonly)=5−nn,n(Aonly)=7−n,n(Bonly)=5−n

n(AUB)=n(Aonly)+n(Bonly)+n(AnB)n(AUB)=n(Aonly)+n(Bonly)+n(AnB)

After you replace the equations in the formula above,

n(AUB)=n(Aonly)+n(Bonly)+n(AnB)n(AUB)=n(Aonly)+n(Bonly)+n(AnB)

n(AUB)=7−n+5−n+nn(AUB)=7−n+5−n+n

Remember our n(AUB)=11,,n(AUB)=11,,

11=7−n+5−n+n