Question

From the given sets, which is an infinite set:

• A. \( \{ x: x \in \mathbb{N} \text{ and } (x - 1)(x - 2) = 0 \} \)
• B. \( \{ x: x \in \mathbb{N} \text{ and } x \text{ is a prime number and less than 199} \} \)
• C. \( \{ x: x \in \mathbb{N} \text{ and } x^5 - 1 = 0 \} \)
• D. \( \{ x: x \in \mathbb{N} \text{ and } x \text{ is odd} \} \)

Hint:

When dealing with sets, check if there is a limit to the number of elements (finite) or if the set extends indefinitely (infinite).

Answer 1

The Correct Option is D

 

Step 1: Analyze the sets. 
- Set 1: \( (x - 1)(x - 2) = 0 \) has solutions \( x = 1 \) or \( x = 2 \), which is a finite set. 

- Set 2: The prime numbers less than 199 are finite, so this is also a finite set. 

- Set 3: \( x^5 - 1 = 0 \) implies \( x = 1 \), which is a finite set. 

- Set 4: The set of odd numbers is infinite because there is no limit to how many odd numbers exist.

Step 2: Conclusion. 
Thus, the infinite set is option 4, which consists of all odd numbers in \( \mathbb{N} \). Therefore, the correct answer is 4. \( \{ x: x \in \mathbb{N} \text{ and } x \text{ is odd} \} \).