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If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?
If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?
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Practice Questions
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Q1
If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?
{1, 2, 3}
{3, 4, 5}
{1, 2, 3, 4, 5}
{1, 2, 5}
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First, A ∩ B = {3}. Then, A ∪ {3} = {1, 2, 3}.
Questions & Step-by-step Solutions
1 item
Q
Q: If A = {1, 2, 3} and B = {3, 4, 5}, what is A ∪ (A ∩ B)?
Solution:
First, A ∩ B = {3}. Then, A ∪ {3} = {1, 2, 3}.
Steps: 6
Show Steps
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}.
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