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Chapter 6: Problem 11

Find \(n(A \cup B)\) given that \(n(A)=6, n(B)=10\), and \(n(A \cap B)=3 .\)

Short Answer

Expert verified
The number of elements in the union of sets A and B is \(n(A \cup B) = n(A) + n(B) - n(A \cap B) = 6 + 10 - 3 = 13\).

Step by step solution

01

Write the given information

We are given: \(n(A)=6\), \(n(B)=10\), \(n(A \cap B)=3\).
02

Apply the formula for finding the union of sets

The formula for finding the number of elements in the union of sets A and B is: \[n(A \cup B) = n(A) + n(B) - n(A \cap B)\]
03

Substitute the given values into the formula

Now, substitute the given values of \(n(A)\), \(n(B)\) and \(n(A \cap B)\) into the formula: \begin{align*} n(A \cup B) &= n(A) + n(B) - n(A \cap B) \\ &= 6 + 10 - 3 \end{align*}
04

Calculate the result

Finally, calculate the value of \(n(A \cup B)\): \[n(A \cup B) = 6 + 10 - 3 = 13\] So, \(n(A \cup B) = 13\).

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