To identify which elements of the set [tex]\( B \)[/tex] are natural numbers, first recall the definition of natural numbers. Natural numbers are the set of positive integers and zero, commonly denoted as [tex]\( \{0, 1, 2, 3, \ldots\} \)[/tex].
Given set [tex]\( B \)[/tex]:
[tex]\[ B = \left\{13, \sqrt{8}, -15, 0, \frac{2}{3}, -\frac{3}{2}, 6.5, \sqrt{4}\right\} \][/tex]
Now, we analyze each element to determine if it is a natural number.
1. 13:
- It is a positive integer.
- Hence, 13 is a natural number.
2. [tex]\(\sqrt{8}\)[/tex]:
- [tex]\(\sqrt{8}\)[/tex] is approximately 2.828, which is not an integer.
- Hence, [tex]\(\sqrt{8}\)[/tex] is not a natural number.
3. -15:
- It is a negative integer.
- Hence, -15 is not a natural number.
4. 0:
- It is a non-negative integer.
- Hence, 0 is a natural number.
5. [tex]\(\frac{2}{3}\)[/tex]:
- It is a fraction, not an integer.
- Hence, [tex]\(\frac{2}{3}\)[/tex] is not a natural number.
6. -[tex]\(\frac{3}{2}\)[/tex]:
- It is a negative fraction.
- Hence, -[tex]\(\frac{3}{2}\)[/tex] is not a natural number.
7. 6.5:
- It is a decimal number, not an integer.
- Hence, 6.5 is not a natural number.
8. [tex]\(\sqrt{4}\)[/tex]:
- [tex]\(\sqrt{4}\)[/tex] is equal to 2, which is an integer.
- Hence, [tex]\(\sqrt{4}\)[/tex] or 2 is a natural number.
Thus, the natural numbers present in the set [tex]\( B \)[/tex] are:
[tex]\[ \{0, 2, 13\} \][/tex]
Therefore, the elements of [tex]\( B \)[/tex] which are natural numbers correspond to option:
B. [tex]\( 13, 0, \sqrt{4} \)[/tex]
Since [tex]\( \sqrt{4} = 2 \)[/tex] is a natural number, so the natural numbers are [tex]\(\{13, 0, 2\}\)[/tex].
Hence, the correct option is B, expressed as [tex]\(\{13, 0, \sqrt{4}\}\)[/tex].
