Math220, Homework 2
Due in class January 18 or 19 (depending on your section)
1. Exercises for Chapter 1: Question 1.22. Let U = {1, 3, 5, . . . , 15} be the universal
set, let A = {1, 5, 9, 13}, and B = {3, 9, 15}. Determine the following:
(a) A ∪ B
(b) A ∩ B
(c) A − B
(d) B − A
(e) A
(f) A ∩ B.
2. Exercises for Chapter 1: Question 1.26. Let U be the universal set and let A, B be
two subsets of U. Draw a Venn diagram for each of the following sets:
(a) A ∪ B
(b) A ∩ B
(c) A ∩ B
(d) A ∪ B
3. Exercises for Chapter 1: Question 1.34. Give an example of two subsets A and B
of {1, 2, 3} such that all of the following are different: A ∪ B, A ∪ B, A ∪ B, A ∪ B, A ∩ B,
A ∩ B, A ∩ B, A ∩ B.
4. Exercises for Chapter 1: Question 1.36. For aSreal number T
r, define Sr to be the
interval [r − 1, r + 2]. Let A = {1, 3, 4}. Determine α∈A Sα and α∈A Sα .
5. Let An = {n, n − 1} for every
natural number
n (so that An is a set of two elements for
S
T
each n ∈ N). Determine n∈N An and n∈N An .
6. Exercises for Chapter 1: Question 1.64. For A = {1, 2} and B = {1}, determine
P(A × B).
7. Exercises for Chapter 1: Question 1.66.
For A = {a ∈ R : |a| ≤ 1} and B = {b ∈ R : |b| = 1}, give a geometric description of the
points in the xy-plane belonging to (A × B) ∪ (B × A).
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