If A={1,2},B={3,4,5}, find `AuuB` and `AcapB`.

Answer

To solve the problem, we need to find the union and intersection of the sets A and B.

**Step 1: Identify the sets.**
- Set A = {1, 2}
- Set B = {3, 4, 5}

**Step 2: Find the union of sets A and B (A ∪ B).**
The union of two sets includes all the elements that are in either set, without duplicating any elements.

- Combine the elements of A and B:
- Elements in A: 1, 2
- Elements in B: 3, 4, 5
- Therefore, A ∪ B = {1, 2, 3, 4, 5}

**Step 3: Find the intersection of sets A and B (A ∩ B).**
The intersection of two sets includes only the elements that are present in both sets.

- Check for common elements between A and B:
- Elements in A: 1, 2
- Elements in B: 3, 4, 5
- There are no common elements between A and B.
- Therefore, A ∩ B = ∅ (the empty set)

**Final Answers:**
- A ∪ B = {1, 2, 3, 4, 5}
- A ∩ B = ∅