Sets Assignment 1 Mathematics in the Modern World, Assignments of Mathematics

Download Sets Assignment 1 Mathematics in the Modern World and more Assignments Mathematics in PDF only on Docsity! Mathematics in the Modern World |. Write T if the statement is true and F if not. T 1. Equal sets are always equivalent sets. F 2. The set of negative integers are finite. F 3. {1, 2, 3,...10} is an infinite set. T 4. {w,a,s,p} ~ {S,w,a,p} T5. lf A{a,e,l,0,u} thenacA T 6. Given C = {x|x e I A 5x <15} and D={x|xe I A x2 < 25}, thenC #D 7. Using the given in problem 6, Q=R. T 8. The set of even numbers less than 100 is infinite. T 9. The cardinality of a null set is zero. F 10. The set of dots in a plane is an infinite set. Il. Tell whether each of the following set is a well-defined set or not. NOT WELL-DEFINED 1. The set of whole numbers more than 407 WELL-DEFINED 2. The set of all months with 31 days NOT WELL-DEFINED 3. The set of competent mathematicians in all state colleges and universities WELL-DEFINED 4. The set of all actors in the movie “Harry Potter’. Ill. Using the Roster Method, list down the elements of each of the following sets described below. 1. A={all elements that belong to the Halogen family } 2. B = {all positive integers between 5 and 10 } 3. C ={ all letters in the word “Philippines” } 4. D ={ all negative odd integers greater than — 13 but less than — 11} ANSWERS: A ={ fluorine, chlorine, bromine, iodine, astatine, tennessine } B={6,7,8,9} C={p,h,li,n,e,s} D={} IV. Using the Rule Method and the Set builder notation to describe each of the following sets whose elements are listed below. 1. D ={ Rudy, crocodile, ™ } 2.A={h,e, 1,0} 3.B={0} 4.C ={2,4,6, ... ,200} ANSWERS: 1. Rudy, crocodile and Tt is the element of D. 2.h, e, |, o is the element of A. 3. B is a null element. 4. The even numbers from 2 to200 is the element of C. V. Tell whether finite or infinite set. INFINITE 1. A ={ set of even numbers} INFINITE 2. B ={ set of integers less than 20} () Q () Q 9. (A-B)’ 10. (B-C)' QO Q QO Q IX. Solve the following problems. Use Venn diagram to answer the questions below: In the College of Engineering, 100 students were asked about their favorite subjects, the result is as follows: 45 liked Algebra 30 liked Chemistry 38 liked English 25 liked both Algebra and Chemistry 26 liked both Algebra and English 22 liked both Chemistry and English 10 like all three subjects a. How many students like Algebra and Chemistry but not English? b. How many students like Algebra and English but not Chemistry? c. How many students like English and Chemistry but not Algebra? d. How many students like exactly 1 subject? e. How many students did not like any subject? X. The Mathematics Club is preparing for year end team building and outing. There are 50 members from which the members of standing committees are taken. There are 8 members of Finance Committee, 5 are members of Program committee and 10 are members of planning committees. Also 4 are also members of Finance and Program, 8 are both members of Finance and Planning and 4 are also members of Program and Planning and 1 of whom was of whom is in Finance too. How many members are on exactly 2 committees? XI. Suppose a survey of 60 freshmen accounting students at the Main Campus of the Polytechnic University of the Philippines produced the following results: 19 of the students read Manila Bulletin Today 18 read Philippine Daily Inquirer 50 read Philippine Star 13 read Manila Bulletin Today and Philippine Daily Inquirer 11 read Philippine Daily Inquirer and Philippine Star 13 read Manila Bulletin Today and Philippine Star 9 read all three. 1. How many students read none of the publications? 2. How many read only Philippine Star? 3. How many read Manila Bulletin Today and Philippine Daily Inquirer, but not Philippine Star? XII. Copy the Venn diagram below and shade the region or region corresponding to the given set. 1.A’ 2,.AUB U U A 3.ANB 4 AnB U U A 5.A'UB U