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Chapter 2: Problem 93

Use the formula for the cardinal number of the union of two sets to solve Exercises 93-96. Set \(A\) contains 17 elements, set \(B\) contains 20 elements, and 6 elements are common to sets \(A\) and \(B\). How many elements are in \(A \cup B\) ?

Short Answer

Expert verified
The cardinal number of the union of sets \(A\) and \(B\) is 31.

Step by step solution

01

Count the number of elements in A and B separately

The number of elements in set \(A\) is 17 and the number of elements in set \(B\) is 20.
02

Identify the elements common to both A and B

The common elements between sets \(A\) and \(B\) are 6.
03

Apply the formula for the cardinal number of the union of two sets

The formula for the cardinal number of the union of two sets is \(|A \cup B| = |A| + |B| - |A \cap B|\). Substitute the values obtained in steps 1 and 2 into the formula to find \(|A \cup B| = 17 + 20 - 6\).

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