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

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

Options:

Correct Answer: {2}

Solution:

The intersection P ∩ Q includes only the even prime number, which is {2}.

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

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

Step 1: Identify the elements of set P. Set P 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 Q. Set Q 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 P and Q. The intersection P ∩ Q includes only the numbers that are in both set P and set Q.
Step 4: Compare the elements of both sets. The only number that is both even (from set P) and prime (from set Q) is 2.
Step 5: Write the intersection. Therefore, P ∩ Q = {2}.

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