Alexander Lee
MAT22AWaldronFall2010
WeBWorK Homework0Background is due : 09/29/2010 at 03:00pm PDT.
Visit
http://www.math.ucdavis.edu/ wally/teaching/22A/22A.html
for the syllabus, grading policy and other information.
The primary purpose of WeBWorK is to let you know that you are getting the correct answer or to alert you if you are making
some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are
having trouble ﬁguring out your error, you should consult the book, or ask a fellow student, one of the TAs or your professor for
help. Don’t spend a lot of time guessing – it’s not very efﬁcient or effective.
Give 4 or 5 signiﬁcant digits for (ﬂoating point) numerical answers. For most problems when entering numerical answers,
you can if you wish enter elementary expressions such as 2
∧
3 instead of 8,
sin
(
3
*
pi
/
2
)
instead of 1,
e
∧
(
ln
(
2
))
instead of 2,
(
2
+
tan
(
3
))
*
(
4

sin
(
5
))
∧
6

7
/
8 instead of 27620.3413, etc. Here’s the
list of the functions
which WeBWorK understands.
You can use the Feedback button on each problem page to send email to the professor.
Logical quantiﬁers
The sentence
A
⇒
B
is read ”A implies B” and means that
whenever A is true, B is also true. That is,
A
⇒
B
means ”if A,
then B.”
For example,
I am in Davis
⇒
I am in California,
because if I am in Davis, then I am in California. Or,
x
is a multiple of four
⇒
x
is even,
because if a number is a multiple of four, then it must surely be
even.
Similarly, the sentence
A
⇐
B
is read ”A is implied by B” and
means that whenever B is true, A is also true. That is,
A
⇐
B
means ”if B, then A,” or, equivalently, ”B only if A.”
For example,
sin
x
=
0
⇐
x
=
0 or

π
,
because if
x
=
0 or
π
then sin
x
=
0
.
The sentence
A
⇒
B
means exactly the same thing as the sen
tence
B
⇐
A
.
Notice that in all of the above examples, we cannot reverse
the arrow. That is, the following statements are FALSE:
I am in California
⇒
I am in Davis.
x
is even
⇒
x
is a multiple of four.
sin
x
=
0
⇒
x
=
0 or

π
.
The ﬁrst is false because if I am in California, I might be in Los
Angeles; the mere fact that I am in California is not enough to
tell me without a doubt that I am in Davis.
The second is false because if a number is even, it does not have
to be a multiple of four–for example, six is even but not a mul
tiple of four.
The third is false because if sin
x
=
0
,
x
could be ANY integer
multiple of
π
,
not just 0 or
π
.
In some situations, we CAN reverse the arrow. That is, some
times
A
⇒
B
AND
B
⇒
A
.
In this case, we write
A
⇐⇒
B
,
read
”A if and only if B.” Sometimes this is abbreviated ”A iff B” in
writing.
For example,