Discrete Mathematics

Answers to Exercises

CHAPTER 1

2. 5

3. 252

4. (i) No (ii) No (iii) Yes (iv) boundary of a unit circle and the relation C is called Circle Relation.

5. 2³⁶, 2⁶(Hint: Number of elements in X × X is 36 and therefore number of possible subsets is 2³⁶. There are 6 elements of the form (a, a) and so the number of reflexive relations is 2⁶.)

7. The relation is not anti-symmetric

8. R = {(1, 1), (2, 2), (3, 3), (4, 4)}

9.

10.

11.

12. (i), since ...