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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 union of sets P and Q?

Options:

  1. {2, 3, 4, 5, 6, 8}
  2. {2, 3, 5, 7}
  3. {2, 4, 6, 8}
  4. {2, 3, 4, 5, 7, 8}

Correct Answer: {2, 3, 4, 5, 7, 8}

Solution: 

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

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

Practice Questions

Q1
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 union of sets P and Q?
  1. {2, 3, 4, 5, 6, 8}
  2. {2, 3, 5, 7}
  3. {2, 4, 6, 8}
  4. {2, 3, 4, 5, 7, 8}

Questions & Step-by-Step Solutions

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 union of sets P and Q?
  • Step 1: Identify the elements of set P. Set P includes all even numbers less than 10. The even numbers are 2, 4, 6, and 8. So, P = {2, 4, 6, 8}.
  • Step 2: Identify the elements of set Q. Set Q includes all prime numbers less than 10. The prime numbers are 2, 3, 5, and 7. So, Q = {2, 3, 5, 7}.
  • Step 3: Find the union of sets P and Q. The union means we combine all unique elements from both sets. We take all elements from P and Q without repeating any numbers.
  • Step 4: Combine the elements: From P we have {2, 4, 6, 8} and from Q we have {2, 3, 5, 7}. When we combine them, we get {2, 3, 4, 5, 6, 7, 8}.
  • Step 5: Write the final answer. The union of sets P and Q is {2, 3, 4, 5, 6, 7, 8}.
  • Set Theory – Understanding the definitions and operations involving sets, specifically union.
  • Even Numbers – Identifying even numbers and their properties.
  • Prime Numbers – Identifying prime numbers and their properties.
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