Question
\( \leftarrow \quad \) Let \( A=\left\{-9,-\frac{12}{4},-\frac{5}{8},-\sqrt{5}, 0, \frac{1}{4}, 5,6 \pi, 3, \sqrt{12}\right\} \). List all the elements of \( A \) that belong to the set of integers.
Ask by Hilton Hobbs. in the United States
Jan 26,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The integers in set \( A \) are \(-9\), \(-3\), \(0\), \(5\), and \(3\).
Solution
To determine which elements of the set \( A \) belong to the set of integers, we need to evaluate each element in \( A \) and check if it is an integer.
The set \( A \) is given as:
\[
A = \left\{-9, -\frac{12}{4}, -\frac{5}{8}, -\sqrt{5}, 0, \frac{1}{4}, 5, 6\pi, 3, \sqrt{12}\right\}
\]
Now, let's evaluate each element:
1. **\(-9\)**: This is an integer.
2. **\(-\frac{12}{4}\)**: This simplifies to \(-3\), which is an integer.
3. **\(-\frac{5}{8}\)**: This is a fraction, not an integer.
4. **\(-\sqrt{5}\)**: This is an irrational number, not an integer.
5. **\(0\)**: This is an integer.
6. **\(\frac{1}{4}\)**: This is a fraction, not an integer.
7. **\(5\)**: This is an integer.
8. **\(6\pi\)**: This is an irrational number (since \(\pi\) is irrational), not an integer.
9. **\(3\)**: This is an integer.
10. **\(\sqrt{12}\)**: This simplifies to \(2\sqrt{3}\), which is an irrational number, not an integer.
Now, we can list the integers found in the set \( A \):
- \(-9\)
- \(-3\)
- \(0\)
- \(5\)
- \(3\)
Thus, the elements of \( A \) that belong to the set of integers are:
\[
\{-9, -3, 0, 5, 3\}
\]
Reviewed and approved by the UpStudy tutoring team
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Bonus Knowledge
The elements of the set \( A \) that belong to the set of integers are \( -9 \), \( 0 \), \( 3 \), and \( 5 \). The integer set is composed of whole numbers, both positive and negative, and \( A \) contains these four integers from its various members.