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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.
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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:

  1. 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.

  2. Now, we need to find the intersection of A' and B'. This is everything that is in both A' and B'.

  3. 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'.

  4. 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.

  5. So, n(A' ∩ B') = n(U) - n(A ∩ B) = 600 - 100 = 500.

So, the answer is "None of these".

This problem has been solved

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