Let A= { 1, 2, 3, 4, 5, 6 }, B= { 2, 4, 5, 6} and C= { 1, 6, 7}. Find
1. A ∩ (B ∪ C)
2. A ∪ (B ∩ C)
3. A ∩ (B ∩ C)
4. A ∪ (B ∪ C)
5. (A ∩ B) ∪ C
6. (A ∩ B) ∩ C
7. (A ∩ B) ∩ (B ∩ C)
8. (A ∪ C) ∩ (B ∪ C)
9. (A ∩ B) ∪ (B ∩ C)

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Answers

2016-06-25T13:14:35+08:00
Intersections (∩) are the common elements in both or all given sets.
Union sets (
∪) are the elements in both or all the given sets. For instance:

1. 
A∩(B∪C)
 - You are looking for the union of sets B and C since they are grouped.
B∪C = {1, 2, 4, 5, 6, 7}
- Next, you are asked to find the intersection of set A and the union of sets B and C.
A∩(B∪C) = {1, 2, 4, 5, 6}

2. 
A∪(B∩C)
B∩C = {6}
A∪(B∩C) = {1, 2, 3, 4, 5, 6}

3. A∩(B∩C)
B∩C = {6}
A∩(B∩C) = {6}

4. A∪(B∪C)
B∪C = {1, 2, 4, 5, 6, 7}
A∪(B∪C) = {1, 2, 3, 4, 5, 6, 7}

5. (A∩B)∪C
A∩B = B
or
A∩B = {2, 4, 5, 6}
(A∩B)∪C = {1, 2, 4, 5, 6, 7}

6. (A∩B)∩C
A∩B = B
or
A∩B {2, 4, 5, 6}
(A∩B)∩C = {6}

7. (A∩B)∩(B∩C)
- You may get the intersection of the either groups first.
A∩B = {2, 4, 5, 6}
B∩C = {6}
(A∩B)∩(B∩C) = {6}

8. (A∪C)∩(B∪C)
A∪C = {1, 2, 3, 4, 5, 6, 7}
B∪C = {1, 2, 4, 5, 6, 7}
(A∪C)∩(B∪C) = {1, 2, 4, 5, 6, 7}

9. (A∩B)∪(B∩C)
A∩B = {2, 4, 5, 6}
B∩C = {6}
(A∩B)∪(B∩C) = {2, 4, 5, 6}
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