If set A = {x | x is an even number less than 10} and set B = {x | x is a prime

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Question: If set A = {x | x is an even number less than 10} and set B = {x | x is a prime number less than 10}, what is A ∩ B?

Options:

Correct Answer: {2}

Solution:

The intersection A ∩ B includes elements that are both even and prime, which is {2}.

If set A = {x | x is an even number less than 10} and set B = {x | x is a prime number less than 10}, what is A ∩ B?

If set A = {x | x is an even number less than 10} and set B = {x | x is a prime number less than 10}, what is A ∩ B?

Step 1: Identify the elements of set A. Set A includes all even numbers less than 10. The even numbers less than 10 are {0, 2, 4, 6, 8}.
Step 2: Identify the elements of set B. Set B includes all prime numbers less than 10. The prime numbers less than 10 are {2, 3, 5, 7}.
Step 3: Find the intersection of sets A and B. The intersection A ∩ B includes elements that are in both set A and set B.
Step 4: Compare the elements of set A and set B. The only number that is both even (from set A) and prime (from set B) is 2.
Step 5: Write the intersection. Therefore, A ∩ B = {2}.

Set Theory – Understanding the definitions and properties of sets, including intersection.
Even Numbers – Identifying even numbers and their properties.
Prime Numbers – Identifying prime numbers and their properties.