Appendix D - Solutions

Summary

2. Sets

1. 2.1 (i) A ∪ B = {1, 2, 3, 4, 5, 9}; (ii) A ∩ B = {1, 3}; (iii) A \ B = {2, 4};(iv) B \ A = {5, 9};(v) Ā = {5, 9}, and B = {2, 4}

2. 2.2 (i) A ∪ B = {0, 1, 2, 3, 5, 6, 9};(ii) A ∩ B = {5}; (iii) A \ B = {0, 2, 6};(iv) B \ A = {1, 3, 9}

3. 2.3 (i) For example see the top part of Figure 2.3; (ii) see Figure 2.2, where A and B are interchanged.

4. 2.4 A ∪ B = R

5. 2.5 A ∪ B = R

6. 2.6 A ∩ B = 1, 2, 3, 4, 5

7. 2.7 A ∩ B = ø

8. 2.8 A ∪ B ∩ C = Z+

9. 2.9 A ∪ B ∩ C = {0, Z-}

10. 2.10 ΩDecimal = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}

11. 2.11 {red, green, blue}

12. 2.12 C

13. 2.13 Z

14. 2.14 {x|5 < x < 10}

15. 2.15 {x |x ∈ R}

3. Probability

1. 3.1 4/52 = 0.077 to 3 s.f.

2. 3.2 0.45%

3. 3.3 20/52 = 0.385 to 3 s.f.

4. 3.4 The probability of the getting an ace followed by a 10 point card, where the other player also gets a 10 point card is 0.72%. The probability of getting an ace followed by a 10 point card, where the other player gets a card with a different value is 1.69%. The total probability of being dealt an ace followed by a 10 point card is the sum: 2.41%.

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