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nature of mathematics

Questions and Answers of Nature Of Mathematics

What do we mean by De Morgan’s laws?
A survey of 100 randomly selected students gave the following information.45 students are taking mathematics.41 students are taking English.40 students are taking history.15 students are taking math
If (P ∪ Q) ∪ R = P ∪ (Q ∪ R) , we say that the operation of union is associative. Is the operation of union for sets an associative operation?
Using the eight regions labeled in Figure 2.14, describe each of the following sets.a. A ∪ Bb. A ∩ Cc. B ∩ Cd. A̅e. A̅ U̅ B̅f. A ∩ B ∩ Cg. A ∪ B ∩ Ch. A̅ U̅ B̅ ∩
Prove A̅ ∪ B̅ = A̅ ∩ B̅.
Verbalize the correct order of operations and then illustrate the combined set operations using Venn diagrams: a. A UB b. AUB
Decide whether each statement in Problems 46–54 is true or false. Give reasons for your answers.a. m ∈ {m, a, t, h}b. {m} ∈ {m, a, t, h}
Decide whether each statement in Problems 46–54 is true or false. Give reasons for your answers.a. {m, a, t, h} ⊆ {m, a, t, h, e, i, c, s}b. {math} ∈ {m, a, t, h}
Tell whether each set in Problems 5–8 is well defined. If it is not well defined, change it so that it is well defined.a. {Good bets on the next race at Hialeah}b. {Years that will be bumper
Tell whether each set in Problems 5–8 is well defined. If it is not well defined, change it so that it is well defined.a. The set of students attending the University of Californiab. {Grains of
An alphamagic square, invented by Lee Sallows, is a magic square such that not only do the numbers spelled out in words form a magic square, but the numbers of letters of the words also form a magic
At the end of each chapter, you will find problems requiring some library research. I hope that as you progress through the course you will find one or more topics that interest you so much that you
a. If the entire population of the world moved to California and each person were given an equal amount of area, how much space would you guess that each person would have (multiple choice)?A. 7
In Problems 41–48, you need to make some assumptions before you estimate your answer. State your assumptions and then calculate the exact answer.“Each year Delta serves 9 million cans of Coke®.
In Problems 41–48, you need to make some assumptions before you estimate your answer. State your assumptions and then calculate the exact answer.A school in Oakland, California, spent $100,000 in
In Problems 41–48, you need to make some assumptions before you estimate your answer. State your assumptions and then calculate the exact answer.The San Francisco Examiner (February 6, 2000, Travel
In Problems 41–48, you need to make some assumptions before you estimate your answer. State your assumptions and then calculate the exact answer.If the U.S. annual production of sugar is 30,000,000
In Problems 41–48, you need to make some assumptions before you estimate your answer. State your assumptions and then calculate the exact answer.Estimate how many pennies it would take to make a
In Problems 41–48, you need to make some assumptions before you estimate your answer. State your assumptions and then calculate the exact answer.Approximately how high would a stack of 1 million $1
In Problems 41–48, you need to make some assumptions before you estimate your answer. State your assumptions and then calculate the exact answer.The Genesis space capsule crashed into the Utah
In Problems 41–48, you need to make some assumptions before you estimate your answer. State your assumptions and then calculate the exact answer.How many classrooms would be necessary to hold
In how many different ways could Melissa get from the YWCA (point A) to the Old U.S. Mint (point M)?
Show that the following sets do not have the same cardinality. {1, 2, 3, 4, 586, 587} {550, 551, 552, 553,..., 902, 903}
Do the following sets have the same cardinality? {48, 49, 50, ,783, 784} {485, 487, 489,..., 2053, 2055}
Classify the following sets as finite or infinite.a. The set of stars in the Milky Wayb. The set of counting numbers greater than two million
Classify the following sets as finite or infinite.a. The set of people who are living or who have ever livedb. The set of grains of sand on all the beaches on Earth
A universal donor is a person who can give blood to any of the blood types , and this is a person with type O- blood. The reason we know this is that the region labeled O- includes all parts of the
Human blood is typed Rh+ (positive blood) or Rh- (negative blood). This Rh factor is called an antigen. There are two other antigens known as A and B types. Blood lacking both A and B types is called
A survey of 70 college students showed the following data:42 had a car; 50 had a TV; 30 had a bicycle; 17 had a car and a bicycle; 35 had a car and a TV; 25 had a TV and a bicycle; 15 had all
In Problems 1–6, let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 9, 10}. Find:a. A ∪ B b. A ∩ Bc. A̅d. B̅
In Problems 1–6, let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 9, 10}. Find:a. |∅|b. |U|c. |A| d. |B|
In Problems 1–6, let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 9, 10}. Find:a. |{0}|b. |A×B|c. |A×U|d. |A×A|
In Problems 1–6, let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 9, 10}. Find:a. A̅ ∩̅ B̅b. A̅ ∪ B̅c. A̅ ∩ B̅d. Does A̅ ∩̅ B̅ = A̅ ∪ B̅ ? Why or
In Problems 1–6, let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 9, 10}. Find:a. (A̅ ∪̅ B̅) ∩̅ A̅b. A̅ ∩ (B ∪ A)
In Problems 1–6, let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}, A = {1, 3, 5, 7, 9}, B = {2, 4, 6, 9, 10}. Find:Replace the question mark with one of the symbols =, ⊂, ⊆, or ∈ to make the statement
If U = {1, 2, 3, . . . , 49, 50}, N = {odd numbers}, and P = {two-digit numbers}, find:a. | N|b. | P|c. |N ∩ P|d. |N ∪ P|
Draw Venn diagrams for the sets in Problems 8–11.a. X ∩ Yb. X ∪ Y
Draw Venn diagrams for the sets in Problems 8–11.a. X̅ b. X̅̅
Draw Venn diagrams for the sets in Problems 8–11.a. X̅ ∩ Yb. X̅ ∪ Y̅
Draw Venn diagrams for the sets in Problems 8–11.a. (X ∩Y) ∩ Zb. (X ∪ Y) ∩ Z
Prove or disprove the statements given in Problems 12–13.A ∪ (B ∩ C) = (A ∪ B) ∩ C
Prove or disprove the statements given in Problems 12–13.(A ∪ B) ∩ C = (A ∩ C) ∪ (B ∩ C)
The set of rational numbers is a. Write this statement in words.b. Give an example for the number q where q ∈ Q. Q = { a = Z,b N}.
Show that the set F = {5, 10, 15, 20, 25, . . .} is infinite.
a. Write the set {-1, -2, -3, . . .} using set-builder notation.b. Show that this set has cardinality 8.
a. What is a logical statement?b. What is a tautology?c. What is the law of contraposition?
Complete the following truth table. P q ~P p^qpVq pq Pq
Construct truth tables for the statements in Problems 3–6. (
Construct truth tables for the statements in Problems 3–6. b~ [d~ (b~ ^d)]
Construct truth tables for the statements in Problems 3–6. [(p ^ q) ^ r] P
Construct truth tables for the statements in Problems 3–6. ~(p ^ q) (~p V ~q)
Give an example of indirect reasoning.
Is the following valid? Pq BE ~q ::~P Can you support your answer?
Give an example of a common fallacy of logic, and show why it is a fallacy.
Write the negation of each of the following statements.a. All birds have feathers. b. Some apples are rotten.c. No car has two wheels.d. Not all smart people attend college.e. If you go on
Consider this statement: “All computers are incapable of self-direction.”a. Translate this statement into symbolic form.b. Write the contrapositive of the statement. Can't you do anything right? D
Which of the following statements are true?a. If 111 + 1 = 1,000, then I’m a monkey’s uncle.b. If 6 + 2 = 10 and 7 + 2 = 9, then 5 + 2 = 7.c. If 6 + 2 = 10 or 5 + 2 = 7, then 7 + 2 = 9.d. If 5 +
a. Using switches, design a circuit that would find the truth values for ∼p ∨ ∼q.b. Using AND-gates, OR-gates, or NOT-gates, design a circuit that would find the truth values for [(p ^ q) ^
Translate into symbols and identify the type of argument.If there are a finite number of primes, then there is some natural number, greater than 1, that is not divisible by any prime.Every natural
If I attend to my duties, I am rewarded.If I am lazy, I am not rewarded.I am lazy.In Problems 17–19, form a valid conclusion using all the premises given in each problem.
All organic food is healthy.All artificial sweeteners are unhealthy.No prune is nonorganic.In Problems 17–19, form a valid conclusion using all the premises given in each problem.
The mathematics department of a very famous two-year college consists of four people: Josie, who is department chairperson; Maureen, Terry, and Warren. For department meetings, they always sit in the
What do we mean when we say that a numeration system is positional? Give examples.
What are some of the characteristics of the Hindu-Arabic numeration system? SOUDAIS ARCHIDE JUARI CARAC drieroindu SMART Vaata FOUR KOPSUC UPD LOUT
Is addition easier in a positional system or in a grouping system? Discuss and show examples.
What do you think computers will be like in the year 2020? Use the history from this chapter, along with your own experiences, to answer this question. Shopping in 2020 www
Briefly discuss some of the events leading up to the invention of the computer.
Discuss some computer abuses.
What are the place value names for the positions A, B, C, and D using the given numeration system? (The fourth position is the separator for the whole number and fractional parts.)a. base 5b. base
Briefly describe each of the given computer terms.a. Hardwareb. Softwarec. Word processingd. Networke. E-mailf. RAMg. Computer bulletin boardh. Hard drive
What are the place value names for the positions A, B, C, and D using the given numeration system. (The fourth position is the separator for the whole number and fractional parts.)a. Hindu-Arabic
Write the given numbers in expanded notation.a. 436.20001b. One billionc. 523eightd. 1001110two
a. Write 4 × 106 + 2 × 104 + 5 × 100 + 6 × 10-1 + 2 × 10-2 in decimal notation.b. Write 3 × 102 + 5 × 10-3 in decimal notation.
Write the numbers in Problems 12–15 in base ten.11101two
Write the numbers in Problems 12–15 in base ten.1111011two
Write the numbers in Problems 12–15 in base ten.122three
Write the numbers in Problems 12–15 in base ten.821twelve
Write the numbers in Problems 16–19 in base two.12
Write the numbers in Problems 16–19 in base two.52
Write the numbers in Problems 16–19 in base two.2007
Write the numbers in Problems 16–19 in base two.one million
a. Write 1,331 in base twelve.b. Write 100 in base five.
Convert the numbers in Problems 49–52 to the binary system.a. 127 eight b. 624 eight
Sketch an abacus to show the numbers given in Problems 49–56.3,214
There is a great deal of concern today about invasion of privacy by computer. With more and more information about all of us being kept in computerized databases, there is the increasing possibility
Convert the numbers in Problems 49–52 to the binary system.a. 5700 eight b. 04320 eight
Sketch an abacus to show the numbers given in Problems 49–56.9,387
Have you ever been told that something cannot be changed because “that is the way the computer does it”? Discuss this issue.
It is stated in the Prologue that “Mathematics is alive and constantly changing.” As we complete the second decade of this century, we stand on the threshold of major changes in the mathematics
In how many different ways could Melissa get from the YWCA (point A) to the St. Francis Hotel (point C in Figure 1.1), using the method of Figure 1.3?Figure 1.1Figure 1.3 Mit CAIR COO Song Male
Find some puzzles, tricks, or magic stunts that are based on mathematics.
What do we mean by exponent?
Write without exponents.a. 105b. 62c. 75d. 263e. 3-2f. 8.90
Compare and contrast the following news clip and the fable in the chapter opening on page 2 with your own experiences in learning mathematics. Perhaps I could best describe my experience of doing
Do some research on Pascal’s triangle, and see how many properties you can discover.You might begin by answering these questions:a. What are the successive powers of 11?b. Where are the natural
What is the sum of the first 100 consecutive odd numbers?
Write a short paper about the construction of magic squares. Figure 1.21 shows a magic square created by Benjamin Franklin.Figure 1.21 52 61 4 13 20 29 20 29 36 45 14 3 62 51 46 35 30 19 21 28 37 44
In how many different ways could Melissa get from the YWCA (point A in Figure 1.1) to the YMCA (point D)?Figure 1.1 Mit CAIR COO Song Male LEYENO 000300 00E www. 0000309 000000000SGOL
Define scientific notation and discuss why it is useful.
Write the given numbers in scientific notation.a. 123,400b. 0.000035c. 1,000,000,000,000d. 7.35

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