Section
2.1: Homework Hints
There are
many problems throughout the text labeled IN YOUR
OWN WORDS. Just relax; do not be afraid to give
your opinion. For the most part, these questions do
not have "right" or "wrong" answers. Several of these
problems ask for examples. Do your best to find examples
that are your own. You should spend about five minutes
in answering each of these questions.
A set is
well defined if there is no disagreement about whether
a particular element is or is not in a given set.
See Example 1.
To designate
a set by roster means to list the elements in a set
(see Example 1). Don't forget that each elements should
be listed only once. For example, in Problem 13a,
do not list the letters m, a, or t
more than once.
You need
to think of a word description for each of these sets.
See Example 2.
These problems
are designed to give you practice with set-builder
notation. First, write down how you might pronounce
the statement, and then list the elements in the set
using the roster method, as shown in Example 1.
Remember
that the empty set is a subset of every set and that
any set is a subset of itself.
In Problem 31 and 32,
work systematically, as shown in Examples 8 and 9.
In Problem 33 and 34, use the results of Problems
31 and 32 to work systematically using patterns.
Remember
that one set divides the universe into two parts.
In Problem 35, the set
of people who are 30 and under is the set, and the
set of people who are over 30 is the complement. Divide
the universe into two parts. Then, draw the set of
drivers as a circle overlapping both parts.
In Problem 36, the set of people who are males,
and the set of people who are females is the complement.
Divide the universe into two parts. Then, draw the
set of bike riders as a circle overlapping both parts.
In Problem 37, the universe is the set of automobiles.
In Problem 38, the universe is the set of communication
devices.
These two
problems require that you understand that cardinality
is the number of elements in a set, that sets are
equivalent if they have the same number of elements,
and are equal if they are the same set. See Examples
4 and 5.
For these
problems you need to distinguish among the symbols
for element, subset, and proper subset. See Example
7.
However, as you go through the book be sure you
look at all the examples in the text. If you need
hints for the Level 3 problems, check some sources
for help on the internet (see the LINKS for that particular
section. As a last resort, you can call the author
at (707) 829-0606.
On the other hand, the problems designated "Problem
Solving" generally require techniques that do not
have textbook examples.
There are many sources for homework help on the internet.
Algebra.help
Here is a site where technology meets mathematics.
You can search a particular topic or choose lessons,
calculators, worksheets for extra practice or other
resources.
http://www.algebrahelp.com/
Ask Dr. Math
Dr. Math is a registered trademark. This is an excellent
site at which you can search to see if your question
has been previously asked, or you can send your question
directly to Dr. Math to receive an answer.
http://mathforum.org/dr/math/
Quick Math
This site provides online graphing calculators. This
is especially useful if you do not have your own calculator.
http://www.quickmath.com/
The Math Forum @ Drexel
This site provides an internet mathematics library
that can help if you need extra help. For additional
homework help at this site, click one of the links in
the right-hand column.
http://mathforum.org/
Mathematics Home Page
Access the Clemens and Alcuins Library of CSB/SJU
and find one of the world's best collections of mathematical
internet sites.
http://library.csbsju.edu/rqs.phtml?subject_id=32
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