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

O a. {x; where x is a positive integers with less than 3 factors)

Ob. {x; where x is an odd number less than 5)

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

Od. (x; Where xeW & 1 <x<4)

Let's analyze each option to determine if it is a subset of the set \(\{x \mid x \text{ is a prime number less than 10}\}\).

The given set is \(\{2, 3, 5, 7\}\), as these are the prime numbers less than 10.

### Option a: \(\{x \mid x \text{ is a positive integer with less than 3 factors}\}\)
- Prime numbers are positive integers with exactly 2 factors (1 and the number itself).
- The prime numbers less than 10 are \(2, 3, 5,\) and \(7\), all of which have exactly 2 factors.
- Therefore, the set \(\{x \mid x \text{ is a positive integer with less than 3 factors}\}\) could be \(\{2, 3, 5, 7\}\), which is the given set itself.

### Option b: \(\{x \mid x \text{ is an odd number less than 5}\}\)
- Odd numbers less than 5 are \(1\) and \(3\).
- The number \(1\) is not a prime number, so this set would be \(\{3\}\).
- Since \(3\) is in the given set, \(\{3\}\) is a subset of \(\{2, 3, 5, 7\}\).

### Option c: \(\{x \mid x \text{ is an odd number less than 10}\}\)
- Odd numbers less than 10 are \(1, 3, 5, 7, 9\).
- From these, \(3, 5,\) and \(7\) are prime numbers, but \(1\) and \(9\) are not prime.
- Therefore, this set would be \(\{3, 5, 7\}\), which is a subset of \(\{2, 3, 5, 7\}\).

### Option d: \(\{x \mid x \in \mathbb{W} \text{ and } 1 < x < 4\}\)
- \(\mathbb{W}\) refers to the set of whole numbers \(\{0, 1, 2, 3, 4, \dots\}\).
- The numbers that satisfy \(1 < x < 4\) are \(2\) and \(3\).
- Both \(2\) and \(3\) are in the given set \(\{2, 3, 5, 7\}\).

### Conclusion:
All the options (\(a\), \(b\), \(c\), and \(d\)) are subsets of the given set \(\{x \mid x \text{ is a prime number less than 10}\}\).

The correct answers are:

- Option \(a\)
- Option \(b\)
- Option \(c\)
- Option \(d\)

Would you like more details on any specific part, or have any questions?

---

Here are 5 related questions to expand your understanding:

1. What are the properties of prime numbers?
2. How do you determine if a set is a subset of another set?
3. What is the difference between whole numbers and natural numbers?
4. Can you find the prime numbers between 10 and 20?
5. How does the concept of factors apply to composite numbers?

**Tip:** A subset of a set can have any number of elements, including all the elements of the original set (making it the same as the original set) or none of them (an empty set).

Explore which options are subsets of the set of prime numbers less than 10. Understand concepts of prime numbers, subset analysis, and logical reasoning in this math problem.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation