Question

If n(A) = 25, n(B) = 40, n(A∪B) = 50 and n(B′) = 25 , find n(A∩B) and n(U).

Answer 1

Solution:-

given by:-
n(A) = 25, n(B) = 40, n(A∪B) = 50 and n(B′) = 25


n(A∩B) = - n(A∪B) -n(A)- n(B)

n(A∩B) =( -50+25+40

= n(A∩B) = 15

n(U) = n(B') +n(B)

n(U) = 25+40 = 65

Answer 2

ANSWER:

n(A∩B)=15, n(U)=65

Step-by-step explanation:

GIVEN THAT:    n(A) = 25

                           n(B) = 40

                           n(A∪B) = 50

                           n(B′) = 25

we know that,

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

putting the values,we get

           50 = 25+ 40 -  n(A∩B)

  solving we get,

       n(A∩B) = 65 -50

       n(A∩B)  = 15      

Also   n(U)= n(B)+n(B)

putting values we get

         n(U)=40 + 25

         n(U)=65