Which one of the following is the subset of set = {x; where x is an prime number less than 10} ?

Choose at least one correct answer

Question 5Answer

a.
{x; where x is an odd number less than 5}

b.
{x; where x is a positive integers with less than 3 factors}

c.
{x; where x is an odd number less than 10}

d.
{x; Where x∈W & 1<x<4}

Let's first identify the set \( S = \{x; \text{where } x \text{ is a prime number less than 10}\} \).

Prime numbers less than 10 are: \( 2, 3, 5, 7 \). 

So, \( S = \{2, 3, 5, 7\} \).

Now, let's analyze each option to see if it is a subset of \( S \):

a. \( \{x; \text{where } x \text{ is an odd number less than 5}\} \)  
   - The odd numbers less than 5 are \( 1, 3 \).
   - Set: \( \{1, 3\} \). 
   - This is **not** a subset of \( S \) because \( 1 \) is not in \( S \).

b. \( \{x; \text{where } x \text{ is a positive integer with less than 3 factors}\} \)  
   - A positive integer with less than 3 factors can only be a prime number (since prime numbers have exactly 2 factors: 1 and the number itself).
   - Set: \( \{2, 3, 5, 7\} \).
   - This is a **subset** of \( S \).

c. \( \{x; \text{where } x \text{ is an odd number less than 10}\} \)  
   - The odd numbers less than 10 are \( 1, 3, 5, 7, 9 \).
   - Set: \( \{1, 3, 5, 7, 9\} \).
   - This is **not** a subset of \( S \) because \( 1 \) and \( 9 \) are not in \( S \).

d. \( \{x; \text{Where } x \in W \text{ and } 1 < x < 4\} \)  
   - The natural numbers greater than 1 and less than 4 are \( 2, 3 \).
   - Set: \( \{2, 3\} \).
   - This is a **subset** of \( S \).

Thus, the correct answers are **b** and **d**.

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Would you like any further details or have any questions? Here are five additional related questions:

1. What is a prime number, and why does it have exactly two factors?
2. Can the set of all prime numbers less than 20 be a subset of another set? Why or why not?
3. How can we determine the number of factors of a given integer?
4. What is the significance of subsets in set theory?
5. Can an empty set be considered a subset of any set?

**Tip:** Remember, every set is a subset of itself, and the empty set is a subset of any set.

Explore and analyze the problem of identifying subsets of prime numbers less than 10. Understand concepts like subsets, prime numbers, and set theory applications. Suitable for high school students learning about sets and prime numbers.

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