Question

If A and B are the subsets of the universalset X and n(x) = 50, n(A) = 35, n(B) = 22 and n(A'∩B') = 3 , find i)n(A∪B) ii) n(A∩B) iii) n(A'∩B)

Answer 1

Answer:

i) n(A ∪ B)  = 45

ii) n(A ∩ B)  = 10

iii) n(A' ∩ B)  = 10

iv) n(A ∩ B') = 25

Step-by-step explanation:

Hi ,

Given n(X) = 50,

n(A) = 35,

n(B) = 20

n(A' ∩ B') = 5

To find

i) n(A ∪ B)  

n(A' ∩ B') = n(X) - n(A∪ B)

⇒n(A∪ B) = n(X) - n(A' ∩ B')

= 50 - 5

= 45

ii) n(A ∩ B)

n(A∪ B) = n(A) + n(B) - n(A∩ B)

n(A∩ B) = n(A) + n(B) - n(A∪ B)

= 35 + 20 - 45

= 10

iii) n(A' ∩ B)  

= n(B) - n(A ∩ B)

= 20 - 10

= 10

iv) n(A ∩ B')

= n(A) - n(A ∩ B)

= 35 - 10

= 25

Hope, it helps !