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Which of the following sets contains only integers?

A. [tex]\left\{1 \frac{3}{7}, 18, -\sqrt{2}, -3, 0\right\}[/tex]

B. [tex]\left\{-1.6, -12, 0.4, \frac{3}{5}, 14\right\}[/tex]

C. [tex]\{-15, -8, -7, 3, 10\}[/tex]

D. [tex]\left\{\sqrt{2}, \sqrt{7}, \pi, 3\pi, \frac{2\pi}{3}\right\}[/tex]

Sagot :

GinnyAnsweridn
To determine which of the given sets contains only integers, we need to evaluate each element within the sets to see if they are all integers.

Let's analyze each set individually:

### Set 1: [tex]\(\left\{1 \frac{3}{7}, 18, -\sqrt{2}, -3, 0\right\}\)[/tex]
- [tex]\(1 \frac{3}{7} = 1 + \frac{3}{7}\)[/tex] is not an integer because [tex]\(\frac{3}{7}\)[/tex] is a non-integer fraction.
- [tex]\(18\)[/tex] is an integer.
- [tex]\(-\sqrt{2}\)[/tex] is not an integer because [tex]\(\sqrt{2}\)[/tex] is an irrational number.
- [tex]\(-3\)[/tex] is an integer.
- [tex]\(0\)[/tex] is an integer.

Since not all elements are integers, this set does not contain only integers.

### Set 2: [tex]\(\left\{-1.6, -12, 0.4, \frac{3}{5}, 14\right\}\)[/tex]
- [tex]\(-1.6\)[/tex] is not an integer because it is a decimal number.
- [tex]\(-12\)[/tex] is an integer.
- [tex]\(0.4\)[/tex] is not an integer because it is a decimal number.
- [tex]\(\frac{3}{5}\)[/tex] is not an integer because it is a fraction.
- [tex]\(14\)[/tex] is an integer.

Since not all elements are integers, this set does not contain only integers.

### Set 3: [tex]\(\{-15, -8, -7, 3, 10\}\)[/tex]
- [tex]\(-15\)[/tex] is an integer.
- [tex]\(-8\)[/tex] is an integer.
- [tex]\(-7\)[/tex] is an integer.
- [tex]\(3\)[/tex] is an integer.
- [tex]\(10\)[/tex] is an integer.

All elements in this set are integers, so this set contains only integers.

### Set 4: [tex]\(\left\{\sqrt{2}, \sqrt{7}, \pi, 3\pi, \frac{2\pi}{3}\right\}\)[/tex]
- [tex]\(\sqrt{2}\)[/tex] is not an integer because it is an irrational number.
- [tex]\(\sqrt{7}\)[/tex] is not an integer because it is an irrational number.
- [tex]\(\pi\)[/tex] is not an integer because it is an irrational number.
- [tex]\(3\pi\)[/tex] is not an integer because it is a multiple of an irrational number.
- [tex]\(\frac{2\pi}{3}\)[/tex] is not an integer because it is a multiple of an irrational number.

Since not all elements are integers, this set does not contain only integers.

### Conclusion
Analyzing the four sets, we find that only Set 3 [tex]\(\{-15, -8, -7, 3, 10\}\)[/tex] contains only integers.
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