To solve this problem, we need to determine which elements of set [tex]\( A \)[/tex] are integers.
1. Analyze each element of set [tex]\( A \)[/tex]:
[tex]\[
A = \left\{-10, -\frac{6}{3}, -\frac{5}{8}, -\sqrt{3}, 0, \frac{1}{4}, 3, 6 \pi, 2, \sqrt{18}\right\}
\][/tex]
2. Check each element to see if it is an integer:
- [tex]\(-10\)[/tex]: This is an integer.
- [tex]\(-\frac{6}{3}\)[/tex]: Simplifies to [tex]\(-2\)[/tex], which is an integer.
- [tex]\(-\frac{5}{8}\)[/tex]: This is a fraction, not an integer.
- [tex]\(-\sqrt{3}\)[/tex]: The square root of 3 is an irrational number, so this is not an integer.
- [tex]\(0\)[/tex]: This is an integer.
- [tex]\(\frac{1}{4}\)[/tex]: This is a fraction, not an integer.
- [tex]\(3\)[/tex]: This is an integer.
- [tex]\(6\pi\)[/tex]: [tex]\(\pi\)[/tex] is an irrational number, so any multiple of [tex]\(\pi\)[/tex] is not an integer.
- [tex]\(2\)[/tex]: This is an integer.
- [tex]\(\sqrt{18}\)[/tex]: The square root of 18 simplifies to [tex]\(3\sqrt{2}\)[/tex], which is not an integer.
3. List the elements that are integers:
The integers in set [tex]\( A \)[/tex] are:
[tex]\[
-10, -2, 0, 3, 2
\][/tex]
4. Match to the choices given:
The list of integers matches the following choices:
- A. [tex]\(-10\)[/tex]
- G. [tex]\(0\)[/tex]
- H. [tex]\(-\frac{6}{3}\)[/tex] (which simplifies to [tex]\(-2\)[/tex])
- E. [tex]\(3\)[/tex]
- J. [tex]\(2\)[/tex]
Based on the detailed analysis, the elements of [tex]\( A \)[/tex] that belong to the set of integers are:
- A. [tex]\(-10\)[/tex]
- G. [tex]\(0\)[/tex]
- H. [tex]\(-\frac{6}{3}\)[/tex]
- E. [tex]\(3\)[/tex]
- J. [tex]\(2\)[/tex]
