Question

If n(A)=36, n(B)=10, n(AU B) = 40 and n(A) = 27 find n(U) and n(AB​

Answer 1

n(A∪B)=n(A)+n(B)−n(A∩B)−−−−−−−(1)

Given n(A)=7

n(B)=9

n(A∪B)=14

Substituting in 1

14=7+9−n(A∩B)

⇒n(A∩B)=16−14=2

Explanation:

ok

Answer 2

The question is incomplete.

It should be:

• If n(A)=36, n(B)=10, n(A∪B)=40, and n(A')=27. Find n(∪) and n(A∩B)

Find n(U)

• n(A') = n(∪) - n(A)
• 27 = n(∪) - 36
• n(∪) = 27 + 36
• n(∪) = 63

Find n(A∩B):

• n(A∪B) = n(A) + n(B) - n(A∩B)
• 40 = 36 + 10 - n(A∩B)
• n(A∩B) = 46 - 40
• n(A∩B) = 6