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Chapter 1: Speaking Mathematically
Section 1.1
6.
a
.
s
is negative
b
. negative; the cube root of
s
is negative (
Or
:
3
√
s
is negative)
c
. is negative;
3
√
s
is negative (
Or
: the cube root of
s
is negative)
9.
a
. have at most two real solutions
b
. has at most two real solutions
c
. has at most two real
solutions
d
. is a quadratic equation; has at most two real solutions
e
.
E
has at most two
real solutions
Section 1.2
6.
T
2
and
T

3
each have two elements, and
T
0
and
T
1
each have one element.
Justiﬁcation
:
T
2
=
{
2
,
2
2
}
=
{
2
,
4
}
,
T

3
=
{
3
,
(

3)
2
}
=
{
3
,
9
}
,
T
1
=
{
1
,
1
2
}
=
{
1
,
1
}
=
{
1
}
, and
T
0
=
{
0
,
0
2
}
=
{
0
,
0
}
=
{
0
}
.
9.
c
. No: The only elements in
{
1
,
2
}
are 1 and 2
,
and
{
2
}
is not equal to either of these.
d
. Yes:
{
3
}
is one of the elements listed in
{
1
,
{
2
}
,
{
3
}}
.
e
. Yes:
{
1
}
is the set whose only element is 1.
g
. Yes: The only element in
{
1
}
is 1, and 1 is an element in
{
1
,
2
}
.
h
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This note was uploaded on 05/10/2011 for the course MATH 325K taught by Professor Shirley during the Spring '11 term at University of Texas at Austin.
 Spring '11
 Shirley
 Math

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