Set Notation Practice Answers

1 Worksheet 1 – Sets 1. Answer (a) 𝐵′ ∩ 𝐴 (b) 𝐵′ ∩ 𝐴′ (c) (𝐴′ ∩ 𝐵′)′ A B A B A B

2 (d) 𝑃 ∪ 𝑄′ (e) (𝑃′ ∪ 𝑄)′ 𝑃′ ∪ 𝑄 is shown below Thus (𝑃′ ∪ 𝑄)′ will be the inverse of above. 2. Answer (a) List all the elements in 𝐴 ∪ 𝐵 in set notation. 𝐴 = {2, 4, 6, 8, 10, 12, 14} 𝐵 = {3, 6, 9, 12, 15} 𝐴 ∪ 𝐵 = {1, 2, 3, 4, 6, 8, 9, 10, 12, 14, 15} (b) List all the elements in 𝐴′ ∪ 𝐵 in set notation. P Q P Q P Q

3 𝐴′ = {1, 3, 5, 7, 9, 11, 13, 15} 𝐴′ ∪ 𝐵 = {1, 3, 5, 6, 7, 9, 11, 12, 13, 15} (c) List all the elements in 𝐴 ∩ 𝐵 in set notation. 𝐴 ∩ 𝐵 = {6, 12} (d) List all the elements in 𝐴′ ∩ 𝐵′ in set notation. 𝐴′ = {1, 3, 5, 7, 9, 11, 13, 15} 𝐵′ = {1, 2, 4, 5, 7, 8, 10, 11, 13, 14} 𝐴′ ∩ 𝐵′ = {1, 5, 7, 11, 13} 3. Answer (a) 𝐴 = {1, 3, 5, 7, 9, 11, 13, 15} 𝐵 = {3, 6, 9, 12, 15} 𝐴 ∩ 𝐵 = {3, 9, 15} (b) 𝐴′ = {2, 4, 6, 8, 10, 12, 14} 𝐵′ = {1, 2, 4, 5, 7, 8, 10, 11, 13, 14} 𝐴! ∩ 𝐵! = {2, 4, 8, 10, 14} (c) Answer A B 1 3 5 7 9 11 13 15 6 12 10 8 4 2 14

4 4. Answer 5. Answer (a) (b) 𝐸′ = {11, 13, 15, 17, 19, 21, 23} 𝑃! = {10, 12, 14, 15, 16, 18, 20, 21, 22} 𝐸′ ∪ 𝑀 = {10, 11, 13, 15, 17, 19, 20, 21, 23} (𝐸! ∪ 𝑀) ∩ 𝑃! = {10, 15, 21}

5 6. Answer (a) 5, 10, 15 (b) (c) {5}, {5, 10}, {5, 15} , {10, 15}, {5, 10, 15} { } 7. Answer

6 8. Answer (a) {4, 5} ⊂ B (b) 2 𝜖 (𝐴 ∪ 𝐵) (c) 𝐵 ∩ 𝐶 = ∅

7 Worksheet 2 – Sets 1. Answer

8 2. Answer 3. Answer (a) 3 Ï C (b) {1} ⊂ (𝐴 ∩ 𝐵) (c) (𝐴 ∪ 𝐵 ∪ 𝐶)′ = ∅

9 4. Answer **Composite number is a positive integer that can be formed by multiplying two smaller positive integers.

10 5. Answer (a) Answer (i) (ii) Only History or Geography = 2 + 12 = 14 (b) Answer (i) 𝐷 ⊂ 𝑃 (ii) There are (some) students who play the drums and the piano. 6. Answer