Let's analyze each set of numbers to determine which set contains integers but not whole numbers or natural numbers.
1. Set 1: [tex]\(\{\sqrt{-1}, \sqrt{-4}, \sqrt{-5}\}\)[/tex]
- These numbers are imaginary numbers because you are taking the square root of a negative number, resulting in imaginary values like [tex]\(i\)[/tex] (the imaginary unit). Hence, this set does not contain integers.
2. Set 2: [tex]\(\left\{\frac{1}{2}, \frac{1}{4}, \frac{1}{8}\right\}\)[/tex]
- These numbers are fractions. Fractions are not integers, as integers are whole numbers without a fractional part. Hence, this set does not contain integers.
3. Set 3: [tex]\(\{-2, -3, -4\}\)[/tex]
- These numbers are negative integers. Integers include both positive and negative whole numbers as well as zero, but whole numbers and natural numbers do not include negative values. Therefore, this set contains integers but not whole numbers (which start from 0) or natural numbers (which start from 1).
4. Set 4: [tex]\(\{0, 1, 2, 3\}\)[/tex]
- These numbers include zero and positive whole numbers. Zero and positive integers are considered whole numbers, and positive integers starting from 1 are also natural numbers. Therefore, this set contains whole numbers and natural numbers.
5. Set 5: [tex]\(\{\sqrt{2}, \pi, \sqrt{3}\}\)[/tex]
- These numbers are irrational numbers. Irrational numbers cannot be expressed as a simple fraction and do not include integers. Hence, this set does not contain integers.
After analyzing all the sets, we find that:
Set 3: [tex]\(\{-2, -3, -4\}\)[/tex] contains integers but not whole numbers or natural numbers.
Therefore, the set that contains integers but not whole numbers or natural numbers is [tex]\( \{-2, -3, -4\} \)[/tex], and the correct set is Set 3.
