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 the difference P - Q?

Options:

Correct Answer: {4, 6, 8}

Solution:

Set P = {2, 4, 6, 8} and set Q = {2, 3, 5, 7}. The difference P - Q = {4, 6, 8}.

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 the difference 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 the difference P - Q?

Step 1: Identify the elements of set P. Set P is defined as the set of even numbers less than 10. The even numbers less than 10 are 2, 4, 6, and 8. So, P = {2, 4, 6, 8}.
Step 2: Identify the elements of set Q. Set Q is defined as the set of prime numbers less than 10. The prime numbers less than 10 are 2, 3, 5, and 7. So, Q = {2, 3, 5, 7}.
Step 3: Find the difference P - Q. The difference of two sets means we take all the elements from set P and remove any elements that are also in set Q.
Step 4: Look at the elements in set P: {2, 4, 6, 8}. Now, check which of these are also in set Q: {2, 3, 5, 7}. The only element in P that is also in Q is 2.
Step 5: Remove the element 2 from set P. After removing 2, the remaining elements in set P are 4, 6, and 8.
Step 6: Write the final result for the difference P - Q. The difference P - Q is {4, 6, 8}.

Set Theory – Understanding the definition of sets, elements, and operations such as set difference.
Even Numbers – Identifying even numbers and their properties.
Prime Numbers – Identifying prime numbers and their properties.