Question

If n(U)=50, n(A)= 30 , n(B)= 18, n((AUB)')=8, find: no of elements in the intersection of A and B​

Answer 1

Answer:

n(A∩B) = 6

Step-by-step explanation:

given, n(U)=50, n(A)= 30 , n(B)= 18, n((A∪B)')=8

now, n((A∪B)') = n(U) - n(A∪B)

⇒n((A∪B)') = 8 = 50 - n(A∪B)

⇒n(A∪B) = -(8 - 50) = -(-42) = 42

now, n(A∪B) = n(A) + n(B) - n(A∩B)

⇒42 = 30 + 18 - n(A∩B)

⇒n(A∩B) = -(42 - 30 - 18) = -(42 - 48) = -(-6) = 6