# 0.11 Sets and counting: homework

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This chapter covers principles of sets and counting. After completing this chapter students should be able to: use set theory and venn diagrams to solve counting problems; use the multiplication axiom to solve counting problems; use permutations to solve counting problems; use combinations to solve counting problems; and use the binomial theorem to expand x+y^n.

## Sets and counting

Find the indicated sets.

List all subsets of the following set.

$\left\{\text{Al, Bob}\right\}$
$\left\{\text{Al, Bob}\right\},\left\{\text{Al}\right\},\left\{\text{Bob}\right\},Ø$

List all subsets of the following set.

$\left\{\text{Al, Bob, Chris}\right\}$

List the elements of the following set.

$\left\{\text{Al, Bob, Chris, Dave}\right\}\cap \left\{\text{Bob, Chris, Dave, Ed}\right\}$
$\left\{\text{Bob, Chris, Dave}\right\}$

List the elements of the following set.

$\left\{\text{Al, Bob, Chris, Dave}\right\}\cup \left\{\text{Bob, Chris, Dave, Ed}\right\}$

In Problems 5 - 8, let $\text{Universal set}=U=\left\{a,b,c,d,e,f,g,h,i,j\right\}$ , $V=\left\{a,e,i,f,h\right\}$ , and $W=\left\{a,c,e,g,i\right\}$ .

List the members of the following sets.

$V\cup W$
$\left\{a,e,i,f,h,c,g\right\}$
$V\cap W$
$\overline{V\cup W}$
$\left\{b,d,j\right\}$
$\stackrel{ˉ}{V}\cap \stackrel{ˉ}{W}$

In 9 - 12, let $\text{Universal set}=U=\left\{1,2,3,4,5,6,7,8,9,\mathrm{10}\right\}$ , $A=\left\{1,2,3,4,5\right\}$ , $B=\left\{1,3,4,6\right\}$ , and $C=\left\{2,4,6\right\}$ .

List the members of the following sets.

$A\cup B$
$\left\{1,2,3,4,5,6\right\}$
$A\cap C$
$\overline{A\cup B}\cap C$

Ø

$\stackrel{ˉ}{A}\cup \overline{B\cap C}$

Find the number of elements in the following sets.

In Mrs. Yamamoto's class of 35 students, 12 students are taking history, 18 are taking English, and 4 are taking both. Draw a Venn diagram and determine how many students are taking neither history nor English?

9 students

In the County of Santa Clara 700,000 people read the San Jose Mercury News, 400,000 people read the San Francisco Examiner, and 100,000 read both newspapers. How many read either the Mercury News or the Examiner?

A survey of athletes revealed that for their minor aches and pains, 30 used aspirin, 50 used ibuprofen, and 15 used both. How many athletes were surveyed?

65

In a survey of computer users, it was found that 50 use HP printers, 30 use IBM printers, 20 use Apple printers, 13 use HP and IBM, 9 use HP and Apple, 7 use IBM and Apple, and 3 use all three. How many use at least one of these Brands?

This quarter, a survey of 100 students at De Anza college finds that 50 take math, 40 take English, and 30 take history. Of these 15 take English and math, 10 take English and history, 10 take math and history, and 5 take all three subjects. Draw a Venn diagram and determine the following.

1. The number of students taking math but not the other two subjects.
2. The number of students taking English or math but not history.
3. The number of students taking none of these subjects.
1. 30
2. 60
3. 10

In a survey of investors it was found that 100 invested in stocks, 60 in mutual funds, and 50 in bonds. Of these, 35 invested in stocks and mutual funds, 30 in mutual funds and bonds, 28 in stocks and bonds, and 20 in all three. Determine the following.

1. The number of investors that participated in the survey.

2. How many invested in stocks or mutual funds but not in bonds?

3. How many invested in exactly one type of investment?

## Tree diagrams and the multiplication axiom

Do the following problems using a tree diagram or the multiplcation axiom.

A man has 3 shirts, and 2 pairs of pants. Use a tree diagram to determine the number of possible outfits.

6

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
If March sales will be up from February by 10%, 15%, and 20% at Place I, Place II, and Place III, respectively, find the expected number of hot dogs, and corn dogs to be sold
8. It is known that 80% of the people wear seat belts, and 5% of the people quit smoking last year. If 4% of the people who wear seat belts quit smoking, are the events, wearing a seat belt and quitting smoking, independent?
Mr. Shamir employs two part-time typists, Inna and Jim for his typing needs. Inna charges $10 an hour and can type 6 pages an hour, while Jim charges$12 an hour and can type 8 pages per hour. Each typist must be employed at least 8 hours per week to keep them on the payroll. If Mr. Shamir has at least 208 pages to be typed, how many hours per week should he employ each student to minimize his typing costs, and what will be the total cost?
At De Anza College, 20% of the students take Finite Mathematics, 30% take Statistics and 10% take both. What percentage of the students take Finite Mathematics or Statistics?

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