If Upper A equals StartSet x vertical line x is an even integer EndSet​, Upper B equals StartSet 4 comma 5 comma 6 comma 7 EndSet​, list the elements of the set Upper A union Upper B.
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Part 1
Choose the correct answer below.
A.StartSet x vertical line x is an even integer or x equals 5 or x equals 7 EndSet
StartSet x vertical line x is an even integer or x equals 5 or x equals 7 EndSet
B.StartSet x vertical line x is an odd integer or x equals 5 or x equals 7 EndSet
StartSet x vertical line x is an odd integer or x equals 5 or x equals 7 EndSet
C.StartSet x vertical line x is an even integer or x equals 4 or x equals 6 EndSet
StartSet x vertical line x is an even integer or x equals 4 or x equals 6 EndSet
D.StartSet x vertical line x is an odd integer or x equals 4 or x equals 6 EndSet
StartSet x vertical line x is an odd integer or x equals 4 or x equals 6 EndSet

Let's first break down the sets:

- Set \( A = \{ x \mid x \text{ is an even integer} \} \), which includes all even integers like \( \ldots, -4, -2, 0, 2, 4, 6, 8, \ldots \).
- Set \( B = \{ 4, 5, 6, 7 \} \).

Now, we need to find the union \( A \cup B \), which means combining all elements from both sets without duplicating any.

- From \( A \), we take all even integers.
- From \( B \), we take \( \{4, 5, 6, 7\} \).

So, the union will be the set of all even integers combined with \( 5 \) and \( 7 \) (since 4 and 6 are already included in the even integers):

\[
A \cup B = \{ x \mid x \text{ is an even integer or } x = 5 \text{ or } x = 7 \}
\]

Thus, the correct answer is:
**A.** \(\{ x \mid x \text{ is an even integer or } x = 5 \text{ or } x = 7 \}\)

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Would you like more details or have any questions?

Here are five related questions for further practice:

1. What is the intersection of sets \( A \) and \( B \)?
2. If \( C = \{2, 3, 6\} \), what is \( A \cup C \)?
3. Can the union of two sets be smaller than either set?
4. How does the union of infinite sets differ from finite sets?
5. What is the symmetric difference between \( A \) and \( B \)?

**Tip:** When finding the union of two sets, always include all distinct elements from both sets.

If A = {x | x is an even integer}, B = {4, 5, 6, 7}, list the elements of the set A union B. Choose the correct answer below: A. {x | x is an even integer or x = 5 or x = 7}, B. {x | x is an odd integer or x = 5 or x = 7}, C. {x | x is an even integer or x = 4 or x = 6}, D. {x | x is an odd integer or x = 4 or x = 6}.

Learn how to find the union of set A, which includes all even integers, and set B = {4, 5, 6, 7}. This problem explains the union of sets and covers concepts in set theory. Suitable for students in Grades 6-8.

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