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n(U)=600,n(A)=460,n(B)=390 and n(AnnB)=3...

`n(U)=600,n(A)=460,n(B)=390` and `n(AnnB)=325` then `n(AuuB)'`

A

75

B

525

C

70

D

155

Text Solution

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The correct Answer is:
To solve the problem, we need to find \( n(A \cup B)' \), which represents the number of elements not in the union of sets A and B. We are given the following values: - \( n(U) = 600 \) (the total number of elements in the universal set) - \( n(A) = 460 \) (the number of elements in set A) - \( n(B) = 390 \) (the number of elements in set B) - \( n(A \cap B) = 325 \) (the number of elements in both sets A and B) ### Step-by-Step Solution: 1. **Use the formula for the union of two sets:** \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] 2. **Substitute the known values into the formula:** \[ n(A \cup B) = 460 + 390 - 325 \] 3. **Calculate the value:** \[ n(A \cup B) = 850 - 325 = 525 \] 4. **Now, find the complement of the union of A and B:** \[ n(A \cup B)' = n(U) - n(A \cup B) \] 5. **Substitute the values:** \[ n(A \cup B)' = 600 - 525 \] 6. **Calculate the final result:** \[ n(A \cup B)' = 75 \] ### Final Answer: \[ n(A \cup B)' = 75 \]
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