If A and B are subsets of the universal set X and n(X) = 50, n(A) = 35, n(B) = 20, n(A' ∩ B') = 5 find:
i) n(A ∪ B)
ii) n(A ∪ B)
iii) n(A' ∩ B)
iv) n(A ∩ B')
Answers
Answered by
198
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 !
Answered by
35
Answer:
Step-by-step explanation:
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
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