Question

If n(A-B)=18, n(AUB)=70, and n(A intersection B)=25 then find n(B)

Answer 1

Given: n(A - B) =18, n(A∪B) =70, n(A ∩ B) =25

n(A∪B) = n(A - B) + n(A ∩ B) + n(B - A) 

   70 = 18 + 25 + n(B - A) 

     70 = 43 + n(B - A) 

     n(B - A) = 70 - 43 

      n(B - A) = 27 

Now n(B) = n(A ∩ B) + n(B - A) 

        n(B)  = 25 + 27 

          n(B)   = 52 

Answer 2

Given:

n(A - B) =18,

n(A∪B) =70,

n(A ∩ B) =25

n(A∪B) = n(A - B) + n(A ∩ B) + n(B - A) 70 = 18 + 25 + n(B - A)

70 = 43 + n(B - A)

n(B - A) = 70 - 43

n(B - A) = 27

Now n(B) = n(A ∩ B) + n(B - A)

n(B) = 25 + 27

n(B) = 52

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