Answer :
To determine which set consists of whole numbers, let's first define what whole numbers are. Whole numbers are the set of non-negative integers, including zero. In mathematical terms, the set of whole numbers is: [tex]\(\{0, 1, 2, 3, \ldots\}\)[/tex].
Now, let's examine each set provided in the question to see which one fits this definition:
1. [tex]\(\{-2, -3, -4\}\)[/tex]
- This set contains negative integers. Whole numbers do not include negative integers, so this set is not the set of whole numbers.
2. [tex]\(\left\{\frac{1}{2}, \frac{1}{4}, \frac{1}{8}\right\}\)[/tex]
- This set contains fractions. Whole numbers are only integers and do not include fractions, so this set is not the set of whole numbers.
3. [tex]\(\{0,1,2,3\}\)[/tex]
- This set includes non-negative integers: 0, 1, 2, and 3. All these numbers fall within the definition of whole numbers.
4. [tex]\(\{\sqrt{-1}, \sqrt{-4}, \sqrt{-5}\}\)[/tex]
- This set contains the square roots of negative numbers which are imaginary numbers. Whole numbers do not include imaginary numbers, so this set is not the set of whole numbers.
5. [tex]\(\{\sqrt{2}, \pi, \sqrt{3}\}\)[/tex]
- This set contains irrational numbers ([tex]\(\sqrt{2}\)[/tex], [tex]\(\pi\)[/tex], and [tex]\(\sqrt{3}\)[/tex]). Whole numbers are only integers and do not include irrational numbers, so this set is not the set of whole numbers.
Upon careful examination, the set [tex]\(\{0,1,2,3\}\)[/tex] fits the definition of whole numbers. Therefore, the set of whole numbers is:
[tex]\[ \{0,1,2,3\} \][/tex]
Conclusively, this set is the third one in the provided list.
Thus, the correct answer is:
[tex]\[ 3 \][/tex]
Now, let's examine each set provided in the question to see which one fits this definition:
1. [tex]\(\{-2, -3, -4\}\)[/tex]
- This set contains negative integers. Whole numbers do not include negative integers, so this set is not the set of whole numbers.
2. [tex]\(\left\{\frac{1}{2}, \frac{1}{4}, \frac{1}{8}\right\}\)[/tex]
- This set contains fractions. Whole numbers are only integers and do not include fractions, so this set is not the set of whole numbers.
3. [tex]\(\{0,1,2,3\}\)[/tex]
- This set includes non-negative integers: 0, 1, 2, and 3. All these numbers fall within the definition of whole numbers.
4. [tex]\(\{\sqrt{-1}, \sqrt{-4}, \sqrt{-5}\}\)[/tex]
- This set contains the square roots of negative numbers which are imaginary numbers. Whole numbers do not include imaginary numbers, so this set is not the set of whole numbers.
5. [tex]\(\{\sqrt{2}, \pi, \sqrt{3}\}\)[/tex]
- This set contains irrational numbers ([tex]\(\sqrt{2}\)[/tex], [tex]\(\pi\)[/tex], and [tex]\(\sqrt{3}\)[/tex]). Whole numbers are only integers and do not include irrational numbers, so this set is not the set of whole numbers.
Upon careful examination, the set [tex]\(\{0,1,2,3\}\)[/tex] fits the definition of whole numbers. Therefore, the set of whole numbers is:
[tex]\[ \{0,1,2,3\} \][/tex]
Conclusively, this set is the third one in the provided list.
Thus, the correct answer is:
[tex]\[ 3 \][/tex]
