Homework Week 2 - Math 101 -3.17.2024
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Regent University *
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Course
101
Subject
Mathematics
Date
Apr 3, 2024
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docx
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Homework Week 2 (Homework)
24SP MATH 101 Mathematics for Liberal Arts (05)
2.
List all subsets of the given set. {yes, no, undecided
}
{ }, {yes}, {no}, {undecided}, {yes, no}, {yes, undecided}, {yes, no, undecided}
{ }, {yes}, {no}, {undecided}, {yes, no}, {yes, undecided}, {no, undecided}
{ }, {yes}, {no}, {yes, no}, {yes, undecided}, {no, undecided}, {yes, no, undecided}
{yes}, {no}, {undecided}, {yes, no}, {yes, undecided}, {no, undecided}, {yes, no, undecided}
L
{ }, {yes}, {no}, {undecided}, {yes, no}, {yes, undecided}, {no, undecided}, {yes, no, undecided}
Identify which subsets are proper.
{ }, {yes}, {no}, {undecided}, {yes, no}, {yes, undecided}, {yes, no, undecided}
{ }, {yes}, {no}, {undecided}, {yes, no}, {yes, undecided}, {no, undecided}
{yes}, {no}, {undecided}, {yes, no}, {yes, undecided}, {no, undecided}, {yes, no, undecided}
{ }, {yes, no}, {yes, undecided}, {no, undecided}, {yes, no, undecided}
{ }, {yes}, {no}, {undecided}, {yes, no}, {yes, undecided}, {no, undecided}, {yes, no, undecided
Identify which subsets are improper.
{ } {yes, no}, {yes, undecided}, {no, undecided}
{ }, {yes}, {no}, {undecided}
{yes}, {no}, {undecided}
{yes, no, undecided}
3.
The universal set is U
= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A
= {1, 2, 3, 4, 5
} and B
= {
4, 5, 6, 7,
8
}, find the following. (Enter your answers as a comma-separated list.)
(a) A
∩
B
{ }
(b) A
∪
B
{ }
(c) A
'
{ }
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(d) B
'
{ }
4.
The universal set is U
= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A
= {
2, 3, 5, 7
} and B
= {
2, 4, 6, 7}, find the following. (Enter your answers as a comma-separated list.)
{ }
(b) A
'
{ }
5
.
The universal set is U
= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}. If A
= {
1, 3, 5, 7, 9
} and B
= {
0, 2, 4, 6, 8
}, find the following. (Enter your answers as a comma-separated list.
)
(a) A
∪
B
{ }
(b) B
'
{ }
6. Use a Venn diagram like the one in the following figure to shade the regions corresponding to the indicated set
.
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7. In a recent transportation survey, 500 high school seniors were asked to check the appropriate box or boxes on the following form.
The results were tabulated as follows:
95
checked the automobile box,
122
checked the motorcycle box, and
28
checked both boxes.
(a) In the above Venn Diagram, Region A represents students owning automobiles and Region M represents students owning motorcycles. Determine each value on the Venn diagram.
x
=
y
=
z
=
w
=
(b) What percent of these students own an automobile or a motorcycle? (Round your answer
to one decimal place.)
%
8. (a) List all subsets of
A
= {
a
}.
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{ }, {
a
}
{ }
{
a
}
How many subsets does
A
have?
______________
(
b) List all subsets of
A
= {
a
,
b
}.
{
a
}, {
b
}
{ }, {
a
}, {
b
}, {
a
,
b
}
{ }, {
a
}, {
b
}
{ }
{
b
}
How many subsets does
A
have?
____________
(c) List all subsets of
A
= {
a
,
b
,
c
}.
{ }, {
a
}, {
b
}, {
c
}, {
a
,
b
}, {
a
,
c
}
{ }, {
a
}, {
b
}, {
c
}, {
a
,
b
}, {
a
,
c
}, {
b
,
c
}, {
a
,
b
,
c
}
{
a
}, {
b
}, {
c
}
{ }, {
a
}, {
b
}, {
a
,
b
}, {
a
,
c
}, {
a
,
b
,
c
}
{
a
}, {
c
}, {
a
,
b
}, {
a
,
c
}, {
a
,
b
,
c
}
How many subsets does
A
have?
_________________________
(d) List all subsets of
A
= {
a
,
b
,
c
,
d
}.
{ }, {
a
}, {
b
}, {
c
}, {
d
}, {
a
,
b
}, {
a
,
c
}, {
b
,
c
}, {
b
,
d
}, {
c
,
d
}, {
a
,
b
,
c
}, {
a
,
b
,
d
}, a
,
c
,
d
}, {
b
,
c
,
d
}
{ }, {
b
}, {
c
}, {
d
}, {
a
,
b
}, {
a
,
c
}, {
a
,
d
}, {
b
,
c
}, {
c
,
d
}, {
a
,
b
,
c
}, {
a
,
c
,
d
}, {
b
,
c
,
d
}, {
a
,
b
,
c
,
d
}
{ }, {
a
}, {
b
}, {
c
}, {
d
}, {
a
,
b
}, {
a
,
c
}, {
a
,
d
}, {
b
,
c
}, {
b
,
d
}, {
c
,
d
}, {
a
,
b
,
c
}, {
a
,
b
,
d
}, {
a
,
c
,
d
}, {
b
,
c
,
d
}, {
a
,
b
,
c
,
d
}
{ }, {
a
}, {
d
}, {
a
,
b
}, {
a
,
c
}, {
a
,
d
}, {
b
,
c
}, {
b
,
d
}, {
a
,
b
,
c
}, {
a
,
b
,
d
}, {
a
,
c
,
d
}, {
b
,
c
,
d
}, {
a
,
b
,
c
,
d
}
{ }, {
a
}, {
b
}, {
c
}, {
d
}, {
a
,
b
}, {
a
,
c
}, {
a
,
d
}, {
b
,
c
}, {
b
,
d
}, {
a
,
b
,
c
}, {
a
,
b
,
d
}, {
b
,
c
,
d
}
How many subsets does A have?
___________________________
(e) Is there a relationship between the cardinal number of set
A
and the number of subsets of set
A
?
Yes
No
(f) How many subsets does
A
= {
a
,
b
,
c
,
d
,
e
,
f
} have?
9. A survey of 200 people yielded the following information:
96
owned a DVD,
129
owned a microwave oven, and
76
owned both. How many people owned the following?
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(a) A DVD or a microwave oven.
(b) A DVD but not a microwave oven.
(c) A microwave oven but not a DVD.
(d) Neither a DVD nor a microwave oven.
10
. In a survey,
674
adults were asked what television programs they had recently watched. The following information was obtained:
222
watched neither the Big Game nor the New Movie, and
289
watched the New Movie. If
183
of those
who watched the New Movie did not watch the Big Game, how many of the surveyed adults watched the following
?
(a) Both programs.
(b) At least one program.
(c) The Big Game.
(d) The Big Game but not the New Movie.
11. Given the sets
U
= {0, 1, 2, 3, 4, 5, 6, 7, 8, 9},
A
= {0, 2, 4, 5, 9}, and
B
= {1, 2, 7, 8, 9}. Use De Morgan's laws to find the set (
A'
U
B
)
'
.
{0, 4, 5}
{0, 2, 3, 4, 5, 6, 9}
{1, 2, 3, 6, 7, 8, 9}
{1, 7, 8}
{7, 8, 9}
12. Which of the following Venn diagrams corresponds to the indicated set?
A
∪
B
∪
C
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13. A yellow die and a brown die are
rolled, and a coin is tossed. Use the Fundamental Principle of Counting to determine how many different outcomes are
possible.
14. Sammy's Sandwich Shop offers a soup, sandwich, and beverage combination at a special price. There are
three sandwiches (turkey, tuna, and tofu)
,
one soup (minestrone)
, and
three beverages (coffee, milk, and mineral water)
to choose from.
(a) Use the Fundamental Principle of Counting to determine how many different meal combinations are possible.
(b) Construct a tree diagram to list all possible soup, sandwich, and beverage combinations. (Do this on paper. Your instructor may ask you to turn in this sketch)
15. If you buy
four
pairs of jeans,
five
sweaters, and
three
pairs of boots, how many new outfits (consisting of a new pair of jeans, a new sweater, and a new pair
of boots) will you have
?
6 | P a g e
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16.
A sandwich shop offers a "U-Chooz" special consisting of your choice of bread, meat, cheese, and special sauce (one each). If there are
five
different breads,
seven
meats,
six
cheeses, and
three
special sauces, how many different sandwiches are possible?
17. How many different Zip Codes are possible using the old style (five digits) and the new style (nine digits)?
old style
New style
18. Find the indicated value. (Simplify the answer as much as possible.)
4!
=
________________.
19. Find the indicated value. (Simplify the answer as much as possible.)
7!
·
3!
=
______________.
20. Find the indicated value. (Simplify the answer as much as possible.)
_________________.
21.
Find the indicated expression, where
n
= 16,
r
= 14. (Simplify the answer as much as possible.)
___________
22. Find the indicated expression, where
n
=
7
,
r
=
5
. (Simplify the answer as much as possible.)
_______________.
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