Question
Find the value of \( n(A \cup B) \) if \( n(A)=10, n(B)=12 \) and \( n(A \cap B)=4 \). \( n(A \cup B)=\square \) (Type a whole number.)
Ask by Best Ortiz. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( n(A \cup B) = 18 \)
Solution
We use the formula for the union of two sets:
\[
n(A \cup B) = n(A) + n(B) - n(A \cap B)
\]
Substitute the given values:
\[
n(A \cup B) = 10 + 12 - 4
\]
Calculate step by step:
\[
10 + 12 = 22
\]
\[
22 - 4 = 18
\]
Thus, the value is:
\[
n(A \cup B)=18
\]
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Simplify this solution Mind Expander
To find the value of \( n(A \cup B) \), we can use the formula: \[ n(A \cup B) = n(A) + n(B) - n(A \cap B) \] Plugging in the given values: \[ n(A \cup B) = 10 + 12 - 4 \] Calculating this gives: \[ n(A \cup B) = 22 - 4 = 18 \] So, \( n(A \cup B) = 18 \).
