Question

If n (ξ) = 40, n (A) = 25, n (B) = 12 and n ((A∪B) ') = 8, find n (A - B) and find n (A∩B).


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Answer 1

Given,

• n(ξ) = 40  

• n(A) = 25  

• n(B) = 12  

• n((A∪B)′) = 8

Here,

• n(A')  = n(ξ)-n(A) = 40-15 = 15

• n(B') = n(ξ)-n(B) = 40-12 = 28

• n((A∩B)′) = n(ξ)-n((A∪B)′) = 40-8 = 32

• n(A∩B) = n(ξ)−n((A∩B)') =40-32 = 8

• n(A∪B) = n(A)+n(B)−n(A∩B) = 25+12-8 = 29

Therefore:

• n(A-B) = n(A)−n(A∩B) = 25-8 = 17

• n(A∩B) = n(ξ)−n((A∩B)') = 8

Answer 2

• Answer:

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