2. Given set A, list all the elements in A that are members of the ff. sets. 8 A = {-√10,-3,-5/2, -0.025, 0, √2, -8/2, e²

a. The Set of Real Numbers

b. The Set of Natural Numbers

C. The Set of Whole Numbers

d. The Set of Integers

e. The Set of Irrational Numbers

Given set \( A = \{-\sqrt{10}, -3, -\frac{5}{2}, -0.025, 0, \sqrt{2}, -\frac{8}{2}, e^2 \} \), let's identify which elements belong to each of the following sets:

### a. **The Set of Real Numbers**
The set of real numbers includes all numbers that are not imaginary or complex. Since all the elements of \( A \) are real, we have:
\[ \{-\sqrt{10}, -3, -\frac{5}{2}, -0.025, 0, \sqrt{2}, -\frac{8}{2}, e^2 \} \]

### b. **The Set of Natural Numbers**
Natural numbers are positive integers (starting from 1). There are no natural numbers in \( A \) because all elements are either negative, zero, or non-integers.

### c. **The Set of Whole Numbers**
Whole numbers include all non-negative integers (0, 1, 2, 3, ...). The only whole number in set \( A \) is:
\[ \{0\} \]

### d. **The Set of Integers**
Integers include both positive and negative whole numbers. The elements of \( A \) that are integers are:
\[ \{-3, 0, -\frac{8}{2} = -4\} \]

### e. **The Set of Irrational Numbers**
Irrational numbers are real numbers that cannot be expressed as a fraction of two integers. The irrational elements of \( A \) are:
\[ \{-\sqrt{10}, \sqrt{2}, e^2\} \]

### Summary of Elements in Each Set:
- **a. Real Numbers:** \( \{-\sqrt{10}, -3, -\frac{5}{2}, -0.025, 0, \sqrt{2}, -\frac{8}{2}, e^2 \} \)
- **b. Natural Numbers:** \( \{\} \) (none)
- **c. Whole Numbers:** \( \{0\} \)
- **d. Integers:** \( \{-3, 0, -4\} \)
- **e. Irrational Numbers:** \( \{-\sqrt{10}, \sqrt{2}, e^2\} \)

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Would you like more details or have any questions?

Here are five related questions:
1. What is the difference between rational and irrational numbers?
2. Can an irrational number be expressed as a repeating decimal?
3. How do you identify if a number is an integer?
4. What makes a number a whole number, and how do they relate to natural numbers?
5. Why is \( e^2 \) considered an irrational number?

**Tip:** An irrational number has a non-repeating, non-terminating decimal expansion.

Given set A, list all the elements in A that are members of the following sets. A = {-√10, -3, -5/2, -0.025, 0, √2, -8/2, e²}. a. The Set of Real Numbers b. The Set of Natural Numbers c. The Set of Whole Numbers d. The Set of Integers e. The Set of Irrational Numbers

Explore how to classify elements of set A into different mathematical sets including Real Numbers, Natural Numbers, Whole Numbers, Integers, and Irrational Numbers. This problem is ideal for students in Grades 7-9 and covers fundamental concepts in set theory and number classifications.

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