Discrete Mathematical Structures

Appendix

ANSWER TO EXERCISES

Chapter 1

1. (a) {1, 2, 3}

   (b) {−1, 1}

   (c) {3, 4, 5, 6}

   (d) {−√2, √2}

   (e) {−2, −1, 0, 1, 2}

2. {6, 12, 30}

3. (a) yes

   (b) yes

   (c) yes

   (d) yes

4. The relation is true

5. (i) equal

   (ii) equal

6. A = {(1, 2, 3), (1, 2, 4), (1, 3, 4), (2, 3, 4)}

7. (a) True

   (b) True

8. Not true as 5 is not even

9. (a) A ∪ B = {1, 2, 3, 5, 6, 7, 8}, A ∩ B = {5}

   (b) A ∪ C = {1, 2, 3, 4, 5, 6, 8}, A ∩ C = {2}

   (c) B ∪ C = {2, 4, 5, 6, 7, 8}, B ∩ C = {6, 8}

10. A ∩ B = {5} = A ∩ C but B ≠ C

12. (a) {5, 6}

   (b) {1, 2, 3},

   (c) φ

   (d) {1, 2, 3}

   (e) {1, 3, 5}

   (f) {1, 2, 3, 5, 6}

15. P(A) = {ϕ, {1}, {2}, {3}, {4}, {1, 2}, {1, 3}, {1, 4}, {2, 3}, {2, 4}, {3, 4}, {1, 2, 3}, {2, 3, 4}, {1, 3, 4}, {1, 2, ...