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If n(A)=8,n(B)=6 and n(A cap B) = 3, the...

If `n(A)=8,n(B)=6 and n(A cap B) = 3`, then `n(A cup B) = ?`

A

6

B

17

C

10

D

None of these

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem, we will use the formula for the number of elements in the union of two sets, which is given by: \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] Where: - \( n(A) \) is the number of elements in set A. - \( n(B) \) is the number of elements in set B. - \( n(A \cap B) \) is the number of elements in the intersection of sets A and B. ### Step-by-Step Solution: 1. **Identify the values given in the problem:** - \( n(A) = 8 \) - \( n(B) = 6 \) - \( n(A \cap B) = 3 \) 2. **Substitute the values into the formula:** \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] \[ n(A \cup B) = 8 + 6 - 3 \] 3. **Perform the addition:** \[ 8 + 6 = 14 \] 4. **Subtract the intersection value:** \[ 14 - 3 = 11 \] 5. **Conclusion:** \[ n(A \cup B) = 11 \] Thus, the number of elements in the union of sets A and B is **11**.
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