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Sagot :
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.
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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