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\( \leftarrow \quad \) 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: \[ \{-9, -3, 0, 5, 3\} \]

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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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