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

Answer:

From the question it is given that,

n(ξ)=40

n(A ′ )=15

n(B)=12

n((A∩B) ′)=32

(i) n(A)We know that, n(A)=n(ξ)−n(A ' )

n(A)=40−15

n(A)=25

(ii) n(B ' )

We know that, n(B ′ )=n(ξ)−n(B)

n(B ′ )=40−12

n(B ′ )=28

(iii) n(A∩B)=n(ξ)−n((A∩B) ' )

=40−32

=8

( iv ) n (A∪B)

=n(A)+n(B)−n(A∩B)

=25+12−8

=37−8

=29

(v)n(A−B)=n(A)−n(A∩B)

=25−8

=17

(vi)n(B−A)

=n(B)−n(A∩B)

=12−8

=4

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