Suppose Set A contains 38 elements and the total number elements in either Set or Set is
67. If the Sets and have 8 elements in common, how many elements are contained in set
B?
Answer
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Ask by Knight Mcdonald. in the United States

Mar 22,2025

Question

Suppose Set A contains 38 elements and the total number elements in either Set or Set is
67. If the Sets and have 8 elements in common, how many elements are contained in set
B?
Answer
Question Help: Message instructor
Calculator
Submit Question

Ask by Knight Mcdonald. in the United States

Mar 22,2025

UpStudy AI · Accepted Answer

Given that the formula for the union of two sets is

$$
|A \cup B| = |A| + |B| - |A \cap B|,
$$

we substitute the known values:

$$
67 = 38 + |B| - 8.
$$

Simplify inside the equation:

$$
38 - 8 = 30,
$$

so the equation becomes

$$
67 = 30 + |B|.
$$

To solve for $$ |B| $$, subtract 30 from both sides:

$$
|B| = 67 - 30 = 37.
$$

Thus, the number of elements in set $$ B $$ is $$ 37 $$.
Set B has 37 elements.