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Ppt sets and set operations

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Introduction to Sets and Set Operations. The presentation include contents of a KWLH Chart, Essential Questions, and Self-Assessment Questions. With exploration and formative assessments.

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Ppt sets and set operations

  1. 1. Mr. Gerald DG BanaagElizabeth Seton School
  2. 2. How do we know when an object isintrinsically part of a set or not? Why dowe have to consider objects as such?Why do you think the study of theconcept of sets important?How is the concept of sets being used inother fields of study?Which is more essential: the learning ofthe concept of sets or the acquisition ofknowledge of the set of real numbers?
  3. 3. KWLH Chart Describe and illustrate well-defined sets,subsets, universal set, and null set. Define and describe the union andintersection of sets and the complement of aset. Use Venn diagram to represent sets, subsets,and set operations. Explain the concept of Venn diagram. Create a Venn diagram of elements classifiedin different sets. Solve problems involving sets.
  4. 4.  Personality Development1. Why do we have to consider ourselves as part of agroup?2. Is it possible for someone to be part of more thanone group?3. Is it beneficial to be part of any group?4. How did you relate the lessons with your personalexperiences as a teenager?5. How do you think these lessons will affect yourpersonality and outlook in life? Learning Process1. How did you learn the lesson on sets?2. Which part of the lesson struck you the most?Why?
  5. 5.  Identify the object that does not belong to thegroup.a. boat, kalesa, car, bus, airplaneb. carabao, chicken, cow, pig, goatc. Camiguin, Bukidnon, Basilan, Cebu, Davao del Surd. hexagon, quadrilateral, rectangle, rhombus,squaree. 2, 12, 24, 11, 30
  6. 6.  How do you know when an object does notbelong to a group? How do we know if a group is considered a set? How do you identify objects that belong to aparticular group? What is your intuitive concept of a set? What do you call objects that belong to a givenset? Can you give everyday experiences that use theconcept of sets? What is the main characteristic of a set inMathematics?
  7. 7. ¤ A group or collection of well-defined distinctobjects is called a __________.When do we say that acollection is “well-defined”?setWhen do we say that anobject belongs to a group?¤ Each object in a set is called a __________or an __________ of a set.memberelement
  8. 8.  Determine whether the following is a set or not:1. The collection of all ESS teachers.2. Tall students in Grade 7.3. Rich people in the Philippines.4. Planets in the Solar System.5. Beautiful girls in the class.6. People living on the moon.7. The collection of all large numbers.8. The set of all multiples of 5.9. A group of good writers.10. Nice people in your class.
  9. 9. “Racism is man’s gravest threat to man - themaximum of hatred for a minimum reason”Abraham J. Heschel(Jewish theologian and philosopher)“At the heart of racism is the religious assertionthat God made a creative mistake when Hebrought some people into being”Friedrich Otto Hertz
  10. 10.  Can you provide possible members of thefollowing groups, if possible?a. Students over 12 years old in the class.b. Counting numbers less than 5.c. Set of letters in the word Philippines.d. Prime numbers which are even.e. Handsome boys in the class.
  11. 11. How do you define the terms containedin a set?When do we know if a set if null orempty?Why do we have to identify whether aset is finite or infinite?How do you think these terms can bepresented?
  12. 12.  The Roster Notation or Listing MethodThis is a method of describing a set by listingeach element of the set inside the symbol { }. Inlisting the elements of the set, each distinctelements is listed once and the order of theelements does not matter.ex. Colors of the rainbowR = {red, orange, yellow, green, blue, indigo, violet}[List the elements in Exploration # 2]
  13. 13.  The Set Builder NotationIt is a method that lists the rules thatdetermine whether an object is an element of theset rather than the actual elements.ex. All cities in the PhilippinesA = {x| x is a city in the Philippines}read as:“A is the set of all x such that x is a city in thePhilippines.”
  14. 14.  Describe the following sets using the specifiedmethods.A. Write a verbal description for each of thefollowing sets:1. D = {1, 3, 5, 7, . . . }2. E = {a, b, c, . . . , z}3. F = {4, 8, 12, 16, . . . , 96}Answer:1. The set of odd numbers.2. The set of small letters in the Englishalphabet.3. The set of multiples of 4 between 0 and 100.
  15. 15.  Describe the following sets using the specifiedmethods.B. List the elements of the following sets:1. M = {x|x > 7, x is an odd integer}2. A = {x|7 < x < 8, x is a counting number}3. T = {x|x is a city in Metro Manila}4. H = {x|x is a counting number between 7 and 10}Answers:1. M = {9, 11, 13, 15, 17, . . . }2. A = { } or 3. T = {Manila, Caloocan, Las Piñas, . . . Pasig}4. H = {8, 9}
  16. 16.  Describe the following sets using the specifiedmethods.C. Write a rule for the following:1. S = {a, e, i, o, u}2. E = {3, 6, 9, . . . , 30}3. T = {Monday, Tuesday, Wednesday, . . . , Sunday}Answers:1. S = {x  x is a vowel in the English alphabet}2. E = {x  3  x  30, x is a multiple of 3}3. T = {x  x is a day in week}
  17. 17. Can you share to the class somenew terms you learned today?Which definition struck you themost?If you can share a topic that youlearned today to a friend, whatwould it be? Why?
  18. 18.  Bring a photo of your favorite actors Define the following:1. Equal2. Equivalent3. cardinality of a set4. Universal Sets5. Subsets

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