1
Sec. 4.1: 4, 5, 9abc, 20, 21, 26, 29, 34, 35, 36, 37
4. Prove that part (iii) of Theorem 1 is true.
Let a, b, and c be integers, where a 6= 0. If a|b and b|c, then a|c.
Let a, b, c Z be arbitrary where a 6= 0. Suppose that a|b and b|c. Then b = aj and
c
1
Sec. 2.1: 5, 10, 18, 19, 21, 22, 32ad, 35, 46
5. Determine whether each of these pair so sets are equal.
(a) cfw_1, 3, 3, 3, 5, 5, 5, 5, 5, cfw_5, 3, 1
Yes, they are equal. Repetition and order doesnt matter for sets.
(b) cfw_1, cfw_1, cfw_1
No, 1 cfw_1
1
Sec. 2.5: 1, 15, 16, 17, 28
1. Determine whether each of these sets is finite, countably infinite, or uncountable. For
those that are countably infinite, exhibit a one-to-one correspondence between the set
of positive integers and that set.
(a) the nega
1
Sec. 2.2: 2, 4, 13, 14, 16, 19a, 24, 29, 32, 34, 35
2. Suppose that A is the set of sophomores at your school and B is the set of students in
discrete mathematics at your school. Express each of theses sets in terms of A and B.
(a) the set of sophomores