Pregunta
\( \leftarrow \quad \) 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
Solución de tutoría real
Respuesta verificada por el tutor
Responder
The integers in set \( A \) are \(-9\), \(-3\), \(0\), \(5\), and \(3\).
Solución
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:
\[
\{-9, -3, 0, 5, 3\}
\]
Revisado y aprobado por el equipo de tutoría de UpStudy
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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.
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