Question: If A = {x | x is a natural number less than 10} and B = {x | x is a prime number}, what is A ∩ B?
Options:
{2, 3, 5, 7}
{1, 2, 3, 4}
{2, 4, 6, 8}
{}
Correct Answer: {2, 3, 5, 7}
Solution:
The intersection A ∩ B includes all prime numbers less than 10, which are {2, 3, 5, 7}.
If A = {x | x is a natural number less than 10} and B = {x | x is a prime number
Practice Questions
Q1
If A = {x | x is a natural number less than 10} and B = {x | x is a prime number}, what is A ∩ B?
{2, 3, 5, 7}
{1, 2, 3, 4}
{2, 4, 6, 8}
{}
Questions & Step-by-Step Solutions
If A = {x | x is a natural number less than 10} and B = {x | x is a prime number}, what is A ∩ B?
Step 1: Identify the set A. A is defined as all natural numbers less than 10. So, A = {1, 2, 3, 4, 5, 6, 7, 8, 9}.
Step 2: Identify the set B. B is defined as all prime numbers. Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves.
Step 3: List the prime numbers less than 10. The prime numbers are 2, 3, 5, and 7.
Step 4: Find the intersection A ∩ B. The intersection includes only the numbers that are in both sets A and B.
Step 5: Compare the elements of A and B. The numbers in A that are also in B are 2, 3, 5, and 7.
Step 6: Write the intersection. Therefore, A ∩ B = {2, 3, 5, 7}.
Set Theory – Understanding the definition and properties of sets, including intersection.
Natural Numbers – Recognizing the set of natural numbers and their properties.
Prime Numbers – Identifying prime numbers and their characteristics.
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