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SETS & VENN DIAGRAMS

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  1. SETS & VENN DIAGRAMS INTRODUCTION

  2. WHAT’S A SET? e.g. 1. M is a set of Math teachers at SMP Madania. 2. P is a set of prime numbers less than 10. 3. _______________________________________________ 4. _______________________________________________ 5. _______________________________________________ A set is a well-defined collection of any kind of objects: people, ideas, plants, numbers, responses, etc.

  3. NOTATION FOR SETS A. LISTING THE ELEMENTS 2. P is the set of whole numbers less than 4. P = {0, 1, 2, 3} 3. ________________________________________________ __ = {________________________} 4. ________________________________________________ __ = {________________________} 5. ________________________________________________ __ = {________________________} 1. M is the set Math teachers at the Lower Secondary Madania. M = {Icha, Tiyan, Wati}

  4. NOTATION FOR SETS B. WRITING THE PROPERTY CHARACTERIZING THE ELEMENTS 1. M is the set Math teachers at SMP Madania. M = {x|x is a Math teacher at SMP Madania} 2. P is the set of whole numbers less than 4. P = {x|x < 4, x  whole numbers} 3. _________________________________________________ __ = {x|x ___________________________} 4. _________________________________________________ __ = {x|x ___________________________} 5. _________________________________________________ __ = {x|x ___________________________}

  5. NOTATION FOR SETS 2. P is the set of whole numbers less than 5. P = {0, 1, 2, 3, 4} P = {x|x < 5, x  whole numbers} →”Pis the set of all numbers xsuch thatx is less than 5, x is element of whole numbers.” 1. M is the set of Math teachers at SMP Madania. M = {Icha, Tiyan, Wati} M = {x|x is a Math teacher at SMP Madania} →”Mis the set of all people xsuch thatx is a Math teacher at SMP Madania.”

  6. NOTATION FOR SETS 4. ______________________________________________. __ = {________________________________} __ = {x|x ___________________________________} →”__ is the set of all xsuch thatx is .” 3. ______________________________________________. __ = {________________________________} __ = {x|x ___________________________________} →”__ is the set of all xsuch thatx is .”

  7. WHAT’S A VENN DIAGRAM?  9 ●1 ●2 ●3 ●5 ●6 ●4 ●9 ●7 ●8 A Venn diagram is a diagram where sets are represented as simple geometric figures, with overlapping and similarity of sets represented by intersections and unions of the figures.

  8. A = The set of multiples of 3 between 0 and 10. → A = {3, 6, 9} B = The set of even numbers between 0 and 10. → B = {2, 4, 6, 8} A B  9 ●1 ●2 ●3 ●5 ●6 ●4 ●9 ●7 ●8 What does this Venn diagram represent?

  9. What do the symbols mean? The set of all individuals in which you are interested is called the universe . U N I V E R S E A B  U = {1, 2, 3, 4, 5, 6, 7, 8, 9} A = The set of multiples of 3 between 0 and 10. → A = {3, 6, 9} B = The set of even numbers between 0 and 10. → B = {2, 4, 6, 8}  9 ●1 ●2 ●3 ●5 ●6 ●4 ●9 ●7 ●8

  10. What do the symbols mean? E L E M E N T & N O T E L E M E N T The objects belonging to a set are called its members or elements. A B 3  A 9 B 4  B 2 A  9 ●1 ●2 ●3 ●5 ●6 ●4 ●9 ●7 ●8

  11. What do the symbols mean? The complementof a set A is the set of all those elements of the universal set which are not in A. C O M P L E M E N T A B B A ~B ~A = {1, 3, 5, 7, 9} = {1,2, 4, 5, 7, 8}  9  9 ●1 ●1 ●8 ●2 ●2 ●3 ●3 ●5 ●5 ●6 ●6 ●4 ●4 ●9 ●9 ●7 ●8 ●7 ●8

  12. What do the symbols mean? The differenceof A and B means the elements which belong to A but not to B. D I F F E R E N C E A A B B B - A A - B = {3, 9} = {2, 4, 8}  9  9 ●1 ●1 ●2 ●2 ●3 ●3 ●8 ●5 ●5 ●6 ●6 ●4 ●4 ●9 ●9 ●7 ●7 ●8 ●8

  13. What do the symbols mean? The intersectionof two sets A and B is the set whose elements are common to both A and B. I N T E R S E C T I O N A B A  B = {6}  9 ●1 ●2 ●3 ●5 ●6 ●4 ●9 ●7 ●8

  14. What do the symbols mean? The unionof two sets A and B is the set which contains all the elements of A and all the elements of B (and hence all the elements which are in both A and B). U N I O N A B A  B = {2, 3, 4, 6, 8, 9}  9 ●1 ●2 ●3 ●5 ●6 ●4 ●9 ●7 ●8

  15. What do the symbols mean? Set A is called a subset of set B if all the elements of A are inside set B. S U B S E T B A B A A = The set of multiples of 4 between 0 and 10. → A = {4, 8} B = The set of even numbers between 0 and 10. → B = {2, 4, 6, 8}  9 ●1 ●2 ●9 ●3 ●5 ●4 ●6 ●8 ●7

  16. What do the symbols mean? If Cand Dhave no common elements, that is, their intersection is the null set/empty set: C  D = Ø, then they are said to be disjoint sets. DISJOINT SETS & NULL/EMPTY SET C = The set of even natural numbers less than 10. → C = {2, 4, 6, 8} D = The set of odd natural numbers less than 10. → D = {1, 3, 5, 7, 9}  9 C // D Ø C D ●4 ●9 ●1 ●6 ●2 ●7 ●3 ●8 ●5

  17. What do the symbols mean? Two sets A and B are said to be equal if they contain exactly the same members. E Q U A L S E T S E = F E = The set of even numbers between 0 and 10. → E = {2, 4, 6, 8} F = The set of multiples of 2 between 0 and 10. → F = {2, 4, 6, 8}  9 E F ●4 ●6 ●2 ●8

  18. What do the symbols mean? E Q U I V A L E N T S E T S E is equivalentwith G if the number of elements in set E is the same as the number of elements in G. E ~ G  13 E = The set of even numbers between 0 and 10. → E = {2, 4, 6, 8} G = The set of four first alphabets. → G = {A, B, C, D} E G ●4 ●C ●6 ●2 ●A ●D ●8 ●B

  19. E Q U I V A L E N T S E T S vs E Q U A L S E T S If A = B, then for sure A ~ B. If A ~ B, then it is possible that A = B

  20. PRESENTING THE NUMBER OF ELEMENTS IN A SET e.g. A = {1, 2, 3, 4} There are 4 elements in set A, then it written as: n(A) = 4