The question asks, "Which of the given number sets contains all integer numbers?"

Let's examine each option to see which set contains only integers:

1. Option 1: $\{\sqrt{4}, -\frac{1}{6}, 9.5\}$

   • $\sqrt{4} = 2$ (an integer).
   • $-\frac{1}{6}$ is a fraction, not an integer.
   • $9.5$ is a decimal, not an integer.
   • So, this set does not contain all integers.

2. Option 2: $\{\sqrt{49}, -1, 0\}$

   • $\sqrt{49} = 7$ (an integer).
   • $-1$ is an integer.
   • $0$ is an integer.
   • So, this set contains all integers.

3. Option 3: $\left\{\frac{10}{4}, 13, \sqrt{20}\right\}$

   • $\frac{10}{4} = 2.5$, not an integer.
   • $13$ is an integer.
   • $\sqrt{20}$ is an irrational number, not an integer.
   • So, this set does not contain all integers.

4. Option 4: $\{-5, \sqrt{0}, \pi\}$

   • $-5$ is an integer.
   • $\sqrt{0} = 0$, which is an integer.
   • $\pi$ is an irrational number, not an integer.
   • So, this set does not contain all integers.

Conclusion:

Option 2 $\{\sqrt{49}, -1, 0\}$ is the correct answer because it contains all integer numbers.

Do you want more details or have any questions?

Here are 5 related questions:

1. What are the properties of integer numbers?
2. How do you identify irrational numbers in a set?
3. What makes a number an integer?
4. Why isn't $\pi$ considered an integer?
5. Can a decimal number ever be an integer?

Tip: Integers include positive and negative whole numbers, including zero, but not fractions, decimals, or irrational numbers.