discrete math weekly quiz
5/6/2020 Math 22 Chapter 3 Quiz: Sp20 MATH F022 DISCRETE MATHEMATICS 02 Witschorik 40299 https://foothillcollege.instructure.com/courses/13425/quizzes/133456 1/9 Math 22 Chapter 3 Quiz 截⽌时间 4⽉29⽇ 23:59 得分 25 问题 16 可⽤ 4⽉29⽇ 19:30 ⾄ 4⽉29⽇ 23:59 ⼤约 4 个⼩时 时间限制 180 分钟 说明 此测验锁定于 4⽉29⽇ 23:59。 尝试历史记录 尝试 时间 分数 最新 尝试 1 127 分钟 24，满分 25 分 正确答案已隐藏。 此测验的分数： 24，满分 25 分 提交时间 4⽉29⽇ 22:44 此尝试进⾏了 127 分钟。 The quiz has 16 questions of types: multiple-choice, numeric-answer, essay, and true/false. Point vary from 1-3 per question. I have to grade the essay questions by hand so you will not have all your points until I do that. 1 / 1 分问题 1 Which of the choices is the truth set for the predicate . [-2,0) U (0,2] (0,4] (0,2] All real numbers between 0 and 2, excluding 0. (-2,0) U (0,2) https://foothillcollege.instructure.com/courses/13425/quizzes/133456/history?version=1 5/6/2020 Math 22 Chapter 3 Quiz: Sp20 MATH F022 DISCRETE MATHEMATICS 02 Witschorik 40299 https://foothillcollege.instructure.com/courses/13425/quizzes/133456 2/9 2 / 2 分问题 2 Identify the one English-language sentence below that is a correct translation of the the following formal statement For all non-zero integers, there exists only one number that when multiplied by the integer gives a product of one. Every integer has a reciprocal. Every integer has an integer reciprocal. For every positive and negative integer you can find at least one rational number that will serve as its reciprocal. We reviewed the definition of a reciprocal in class. 2 / 2 分问题 3 Consider the English-language statement, Being at least 35 years old is a necessary condition for being president of the United States. Which one of the following statements is not a valid rewriting of the original statement? For any person x, if x is president of the United States, then x is at least 35 years old. Considering all people, a person, denoted p, can be president of the United States only if the person p is at least 35 years old. 5/6/2020 Math 22 Chapter 3 Quiz: Sp20 MATH F022 DISCRETE MATHEMATICS 02 Witschorik 40299 https://foothillcollege.instructure.com/courses/13425/quizzes/133456 3/9 For any person denoted as p, if p is younger than 35, then p cannot be president of the United States. To be president of the United States it is sufficient that the candidate be at least 35 years old. 35 years old is a necessary, but not sufficient qualification. For example, the candidate must also be a natural born citizen. 2 / 2 分问题 4 Consider the statement Which one of the following has an equivalent meaning? Only the letters used for the symbols have been changed. 2 / 2 分问题 5 If compilation of a computer program produces error messages, then the program is not correct. Compilation of this program does not produce error messages. 5/6/2020 Math 22 Chapter 3 Quiz: Sp20 MATH F022 DISCRETE MATHEMATICS 02 Witschorik 40299 https://foothillcollege.instructure.com/courses/13425/quizzes/133456 4/9 This program is correct. Which one of the following is true for this argument? The argument is invalid and exhibits the converse error. The argument is valid by universal modus tollens. The argument is invalid and exhibits the inverse error. The inverse of p->q is ~p->~q and is not a valid argument form. The argument is valid by universal modus ponens. 2 / 2 分问题 6 Which one of the following arguments is invalid? No polynomial functions have horizontal asymptotes. This function has a horizontal asymptote. This function is not a polynomial function. Any function that is a polynomial will not approach a fixed value as its input grows without bound, positive or negative. This function approaches the value 0 as its input grow without bound in both the positive and negative directions. This function is not a polynomial No polynomial functions have horizontal asymptotes. This function is a polynomial function. This function does not have a horizontal asymptote. No polynomial functions have horizontal asymptotes. This function does not have a horizontal asymptote. This function is a polynomial function. 5/6/2020 Math 22 Chapter 3 Quiz: Sp20 MATH F022 DISCRETE MATHEMATICS 02 Witschorik 40299 https://foothillcollege.instructure.com/courses/13425/quizzes/133456 5/9 For p->q, it is not always true that ~q->p 2 / 2 分问题 7 您的答案： Translate this formal statement into an English-language sentence with the same meaning. For any x in the set of all real numbers, there exists an n in the set of all integers such that n is greater than x. This statement is called the Archimedean principle. For every real number there exists an integer that exceeds it. 2 / 2 分问题 8 您的答案： Negate the following statement and give your answer as an English-language sentence. There exist x in the set of all integers such that for all y, an element(s) of all integers, x plus y equals y plus x equals y, and x is not equal to zero. There exists an integer x which added to any integer y, in any order, create a summation equal to y and x is not equal to zero. 5/6/2020 Math 22 Chapter 3 Quiz: Sp20 MATH F022 DISCRETE MATHEMATICS 02 Witschorik 40299 https://foothillcollege.instructure.com/courses/13425/quizzes/133456 6/9 2 / 2 分问题 9 您的答案： Create a universal condition statement in the integers that is vacuously true. For any y in the set of all negative integers, if x equals to zero, the square of x equals to negative one. There are many different answers. One example is "For all x an integer, if x>x, then 0 = 1." 2 / 2 分问题 10 您的答案： The computer scientists Richard Conway and David Gries one wrote: The absence of error messages during translation of a computer program is only a necessary and not a sufficient condition for reasonable [program] correctness. Rewrite this statement without using the words necessary or sufficient. There are reasonable [program] incorrectness(es) if there exist error messages during the translation of a computer program. Reasonable program correctness requires the absence of error messages during translation of a computer program but it does not guarantee correctness. What about the not sufficient part? 5/6/2020 Math 22 Chapter 3 Quiz: Sp20 MATH F022 DISCRETE MATHEMATICS 02 Witschorik 40299 https://foothillcollege.instructure.com/courses/13425/quizzes/133456 7/9 0 / 1 分问题 11错误错误 Is the following statement true or false? True Whatever y you think works for all x, choose x = 0 and you must have 0 <= z=""><=0 for all z. false 1 / 1 分问题 12 for the negation of a universal conditional, , to be true, you cannot have any such that true false it is only required that there exist at least one such that 1 / 1 分问题 13 a frequent-flyer club brochure states, "you may select among carriers only if they offer the same lowest fare." assuming that "only if" has its formal, logical meaning and that the hypothesis and conclusion are both true, we can conclude from the statement that that if two carriers offer the same lowest fare, the customers will be free to choose between the two. 5/6/2020 math 22 chapter 3 quiz: sp20 math f022 discrete mathematics 02 witschorik 40299 https://foothillcollege.instructure.com/courses/13425/quizzes/133456 8/9 true false converse error. 1 / 1 分问题 14 a predicate is a sentence that contains a finite number of variables and becomes a statement when specific values, from a specific domain, are substituted for the variables. true book definition of predicate. false 1 / 1 分问题 15 the negation of the statement is the statement true false retain the domain. 5/6/2020 math 22 chapter 3 quiz: sp20 math f022 discrete mathematics 02 witschorik 40299 https://foothillcollege.instructure.com/courses/13425/quizzes/133456 9/9 1 / 1 分问题 16 in this question, is the set of the digits in your eight-digit student id, for example if your student id is 20119987 then . evaluate the following multiply quantified statement using populated from the digits in your student id. true every set of digits from a student id will have a maximum and a minimum digit that are distinct. false 测验分数： 24，满分 25 分 for="" all="" z.="" false="" 1="" 1="" 分问题="" 12="" for="" the="" negation="" of="" a="" universal="" conditional,="" ,="" to="" be="" true,="" you="" cannot="" have="" any="" such="" that="" true="" false="" it="" is="" only="" required="" that="" there="" exist="" at="" least="" one="" such="" that="" 1="" 1="" 分问题="" 13="" a="" frequent-flyer="" club="" brochure="" states,="" "you="" may="" select="" among="" carriers="" only="" if="" they="" offer="" the="" same="" lowest="" fare."="" assuming="" that="" "only="" if"="" has="" its="" formal,="" logical="" meaning="" and="" that="" the="" hypothesis="" and="" conclusion="" are="" both="" true,="" we="" can="" conclude="" from="" the="" statement="" that="" that="" if="" two="" carriers="" offer="" the="" same="" lowest="" fare,="" the="" customers="" will="" be="" free="" to="" choose="" between="" the="" two.="" 5/6/2020="" math="" 22="" chapter="" 3="" quiz:="" sp20="" math="" f022="" discrete="" mathematics="" 02="" witschorik="" 40299="" https://foothillcollege.instructure.com/courses/13425/quizzes/133456="" 8/9="" true="" false="" converse="" error.="" 1="" 1="" 分问题="" 14="" a="" predicate="" is="" a="" sentence="" that="" contains="" a="" finite="" number="" of="" variables="" and="" becomes="" a="" statement="" when="" specific="" values,="" from="" a="" specific="" domain,="" are="" substituted="" for="" the="" variables.="" true="" book="" definition="" of="" predicate.="" false="" 1="" 1="" 分问题="" 15="" the="" negation="" of="" the="" statement="" is="" the="" statement="" true="" false="" retain="" the="" domain.="" 5/6/2020="" math="" 22="" chapter="" 3="" quiz:="" sp20="" math="" f022="" discrete="" mathematics="" 02="" witschorik="" 40299="" https://foothillcollege.instructure.com/courses/13425/quizzes/133456="" 9/9="" 1="" 1="" 分问题="" 16="" in="" this="" question,="" is="" the="" set="" of="" the="" digits="" in="" your="" eight-digit="" student="" id,="" for="" example="" if="" your="" student="" id="" is="" 20119987="" then="" .="" evaluate="" the="" following="" multiply="" quantified="" statement="" using="" populated="" from="" the="" digits="" in="" your="" student="" id.="" true="" every="" set="" of="" digits="" from="" a="" student="" id="" will="" have="" a="" maximum="" and="" a="" minimum="" digit="" that="" are="" distinct.="" false="" 测验分数：="" 24，满分="" 25="">