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.
