Let n(U) = 600, n(A) = 200, n(B) = 300, n(A Ç B) = 100, then n(A¢ Ç B¢) is equal to— 400 600 200 None of these.
Question
Let n(U) = 600, n(A) = 200, n(B) = 300, n(A Ç B) = 100, then n(A¢ Ç B¢) is equal to—
- 400
- 600
- 200
- None of these.
Solution
The question is asking for the number of elements in the intersection of the complements of sets A and B.
Here's how you can solve it:
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First, find the complements of A and B. The complement of a set is everything in the universal set that is not in the set. So, n(A') = n(U) - n(A) = 600 - 200 = 400 and n(B') = n(U) - n(B) = 600 - 300 = 300.
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Now, we need to find the intersection of A' and B'. This is everything that is in both A' and B'.
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However, we can't just add n(A') and n(B') together, because then we would be counting twice the elements that are in both A' and B'.
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So, we need to subtract out the elements that are in both A' and B'. But this is just the complement of the intersection of A and B, which is everything in the universal set that is not in A ∩ B.
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So, n(A' ∩ B') = n(U) - n(A ∩ B) = 600 - 100 = 500.
So, the answer is "None of these".
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