Which of the following is an example of a finite set?
Responses

A	R = {2, 4, 6, 8, 10}R = {2, 4, 6, 8, 10}

B	Q = {x∣x is a natural number}Q = {x ∣ x is a natural number}

C	V = {x∣x is an even number}V = {x ∣ x is an even number}

D	T = {x∣x is a real number}

To determine which of the sets provided is finite, we need to analyze the definitions:

- **A: \( R = \{2, 4, 6, 8, 10\} \)**: This is a set with exactly five elements, which makes it a **finite set**.

- **B: \( Q = \{x \mid x \text{ is a natural number}\} \)**: The natural numbers \( \{1, 2, 3, 4, 5, \dots\} \) go on infinitely, so this is an **infinite set**.

- **C: \( V = \{x \mid x \text{ is an even number}\} \)**: Even numbers \( \{2, 4, 6, 8, \dots\} \) also go on infinitely, so this is an **infinite set**.

- **D: \( T = \{x \mid x \text{ is a real number}\} \)**: The real numbers cover all numbers on the number line (including rational and irrational numbers), so this is an **infinite set**.

### Conclusion:
The correct answer is **A**: \( R = \{2, 4, 6, 8, 10\} \), which is a **finite set**.

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Do you have any questions or would you like more details on this concept?

### Related Questions:
1. What is the definition of a finite set?
2. How can you determine if a set is infinite?
3. Are there any types of sets that are neither finite nor infinite?
4. Can the set of integers be considered finite or infinite?
5. What is the difference between natural numbers and real numbers?

### Tip:
Finite sets have a countable number of elements, while infinite sets extend indefinitely.

Which of the following is an example of a finite set?
A: R = {2, 4, 6, 8, 10}
B: Q = {x | x is a natural number}
C: V = {x | x is an even number}
D: T = {x | x is a real number}

Discover the concept of finite and infinite sets through the example of R = {2, 4, 6, 8, 10}. This problem introduces key set theory concepts and distinguishes between finite and infinite sets. Ideal for students in Grades 6-8.

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