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If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?

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Question: If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?

Options:

  1. {1, 2, 3}
  2. {3, 4, 5}
  3. {1, 2, 3, 4, 5}
  4. {1, 2, 5}

Correct Answer: {1, 2, 3}

Solution: 

First, A ∩ B = {3}. Then, A ∪ {3} = {1, 2, 3}.

If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?

Practice Questions

Q1
If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?
  1. {1, 2, 3}
  2. {3, 4, 5}
  3. {1, 2, 3, 4, 5}
  4. {1, 2, 5}

Questions & Step-by-Step Solutions

If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?
Correct Answer: {1, 2, 3}
  • Step 1: Identify the sets A and B. A = {1, 2, 3} and B = {3, 4, 5}.
  • Step 2: Find the intersection of A and B, which is A ∩ B. This means we look for elements that are in both A and B.
  • Step 3: The only element that is in both A and B is 3. So, A ∩ B = {3}.
  • Step 4: Now, we need to find the union of A and the intersection we just found. This means we combine all elements from A and {3}.
  • Step 5: A = {1, 2, 3} and {3} together gives us {1, 2, 3}.
  • Step 6: Therefore, A ∪ (A ∩ B) = {1, 2, 3}.
  • Set Operations – Understanding union (∪) and intersection (∩) of sets.
  • Set Notation – Properly interpreting and manipulating set notation.
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