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.