Section 6.1

#4 Only the relation in part (a) is irreflexive. Others are all reflexive.

#28

Section 6.3

#4

Property	(a)	(b)	(c)
Reflexive	Yes	No	No
Irreflexive	No	No (all diagonal entries are not zero)	No
Symmetric	Yes	No	Yes
Antisymmetric	No	Yes	No
Transitive	Yes	Yes (trivially)	No (Contains (2,1) and (1,2) but not (2,2)

#9

Check your solutions guide.

Section 6.5

#4

One example: All the students born in the same province. Equivalence classes will be non-empty sets of students from each province.

You are supposed to give three such examples.

#26

b (0 is in neither one of the states) and e (4 is in both the sets) are not partitions. All the others are partitions

Section 6.6

1. l, m
2. a, b, c
3. doesn't exist
4. doesn't exist
5. k, l, m
6. k
7. none
8. doesn't exist