Worksheet Chapter 4: Operations on Sets

1. Given sets P = {1, 2, 3, 4}, Q = {3, 4, 5, 6}, and R = {4, 6, 7, 8}. Find the elements of: (a) P ∩ Q ∩ R (b) (P ∪ Q) ∩ R

2. A group of 50 tourists were surveyed about their visits to two towns, Town X and Town Y. 30 visited Town X, 25 visited Town Y, and 10 visited both towns. (a) Draw or describe a Venn diagram representing this scenario. (b) Calculate how many tourists visited ONLY Town X. (c) Calculate how many tourists did not visit either town.

3. Given universal set ξ = {x : 10 ≤ x ≤ 20, x is an integer}, set A = {multiples of 3}, and set B = {multiples of 4}. Find (A ∪ B)'.

4. True or False: If A ∩ B = ∅, then set A and set B have no common elements.

5. Given that n(ξ) = 100, n(A) = 55, n(B) = 40, and n(A ∩ B) = 15. (a) Find n(A ∪ B). (b) Find n(A' ∩ B').

6. Which of the following identities correctly expresses De Morgan's Law for set operations?

7. Fill in the blank: The set of all elements that belong to either Set A or Set B or both is called the ________ of sets.

8. In a school club of 60 pupils, 32 play Chess (C), 28 play Scrabble (S), and 24 play Carrom (K). It is known that 12 play Chess and Scrabble, 10 play Scrabble and Carrom, 8 play Chess and Carrom, and 4 play all three games. (a) Calculate how many pupils play Chess ONLY. (b) Calculate how many pupils do NOT play any of the three games.

9. True or False: For any set A, A ∪ A' = ξ (the universal set).

10. Given universal set ξ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, set P = {x : x is a prime number}, and set Q = {x : x is an odd number}. (a) List all elements of set P ∩ Q. (b) Find n(P ∩ Q).