Homework #6

1. Section 4.3, 2 (p. 186)

2. Section 4.3, 4 (p. 186)

3. Section 4.3, 6 (p. 187)

4. Section 4.3, 11

5. Section 4.3, 14

6. Let A be the set of ordered pairs of positive integers, and define relation R on A as follows:

(a, b)R(c, d) if and only if a+d = b+c.

Prove that R is an equivalence relation.

7. Let A be the integers, and let R be congruence mod 5 relation. Give the equivalence class for 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10. How many distinct equivalence classes does R have?

8. Give an example of a relation R on a set A that is reflexive, anti-symmetric and transitive. (Define both A and R). Draw the digraph for R.

9. Let A = {1, 2, 3, 4} and define relation R on A as follows:

xRy if and only if 2x <= y. Define the relation RR, and draw the digraph of R and the digraph of RR.