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}