Much of mathematics, including probability and statistics, is ultimately based upon set theory. So it is important to have a thorough understanding of this topic. Set theory is the study of collections of objects called elements. These elements can be combined using set operations of union, intersection and complement.
Given the sets A = {1, 2, 3, 4, 5}, B = {6, 7, 8, 9, 10}, C = {1, 3, 5, 7, 9}, D = {2, 4, 6, 8, 10}, E = {3, 4, 5, 6, 7}, F = {3, 4, 5},and universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, test your knowledge about sets by stating which of the following are true and which are false. Here are solutions to the worksheet so that you can check your work.
- A = B
- A = A
- C ⊆ E
- F ⊆ E
- E ⊆ F
- D ⊆ U
- Ø ⊆ F
- Ø ⊆ Ø
- Ø ∈ A
- 1 ∈ A
- 7 ∈ A
- 3 ∉ D
- 3 ∉ A
- F ∈ E
- 1 ∉ B
- Ø ∈ Ø
- Ø ∈ {Ø}
- AC = B
- ØC = U
- A ∪ B = C
- A ∩ B = C
- A ∪ B = U
- A ∩ E = F
- B ∪ C = {7, 9}
- B ∩ C = {7, 9}
- B ∩ F = Ø
- F ∪ Ø = F
- E ∩ Ø = Ø
- D ∪ U = D
- (A ∪ B )C = A C ∩ B C
