Operations on sets

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Operations on sets

  1. 1. OPERATIONS ON SETS by: Teacher MYRA CONCEPCION
  2. 2. UNDERSTANDING UNIVERSAL SETS … A B C D E F G H I J K L M N O P Q R S T U V W X Y Z <ul><li>… -5 -4 </li></ul><ul><li>-3 -2 </li></ul><ul><li>-1 0 1 </li></ul><ul><li>3 4 5 </li></ul><ul><li>6 7 </li></ul><ul><li>8 9 </li></ul><ul><li>10 11 12 </li></ul><ul><li>13 14 15 … </li></ul>A = {f,r,e,s,h,m,a,n} B = {1,4,3}
  3. 3. UNIVERSAL SET is where all the sets belong. In other words, all sets are a subset of Universal Set. REMEMBER: U is the symbol for universal set !
  4. 4. If a set consists of elements such as Philippines, Korea, United States and France , what could be the universal set? The universal set is consist of COUNTRIES!
  5. 5. UNDERSTANDING COMPLEMENTS OF A SET … c r u s h U A A = {c,r,u,s,h} or A = {x|x is a letter in the word “crush”} A’ ={a,b,d,e,f,g,i,j,k,l,m,n,o,p,q,t,v,w,x,y,z}
  6. 6. COMPLEMENT OF A SET is a set of elements that can be found in U but not in a certain set. It is denoted by ’ . In other words, complements of a set are elements that are OUT OF PLACE! FYI: There is another symbol for complement of a set!
  7. 7. If a set consists of letters in the sentence “ The quick brown fox jumps over the lazy dog.” , what could be its complement to U ? There will be no complement! The sentence consists all the letters of the English alphabet.
  8. 8. UNDERSTANDING COMPLEMENTS OF A SET … A = {1,2,4,5,7} B = {1,3,5,6} A – B The complement of B with respect to A. = {2,4,7} B – A The complement of A with respect to B. = {3,6}
  9. 9. What is F – B if F = {t,e,a,c,h} and B = {m,a,t,h}? The complements of B with respect to F are elements e and c .
  10. 10. UNDERSTANDING UNION OF SETS … A = {1,2,3,4,5} B = {2,4,6,8} A U B U C = {1,2,3,4,5,6,8} C = {1,3,5,7,9} A U B = {1,2,3,4,5,6,7,8,9}
  11. 11. UNION OF SETS is the set containing all the elements found in the sets being compared. It is denoted by U . In other words, union of sets is simply combing the elements of the sets! REMEMBER: Do not duplicate or repeat elements! DISTINCT
  12. 12. What is the union of sets P and C if P = {d,o,w,n} and C = {l,o,a,d}? P U C = {d,o,w,n,l,a,}
  13. 13. UNDERSTANDING INTERSECTION OF SETS … 1 3 5 U A A = {1,2,3,4,5} or A = {x|x is a number from 1 to 5} B = {2,4,6,8} or B = {x|x is a positive one-digit number} A ∩ B 6 8 2 4 B = {2,4}
  14. 14. INTERSECTION OF SETS is the set of all subsets that belongs to the two sets being compared. It is denoted by ∩. In other words, intersection of sets are the common elements for both sets. REMEMBER: Element should be seen on both sets!
  15. 15. What is the intersection of sets A and I if A = {c,l,a,r,k,s,o,n} and I = {d,a,u,g,h,t,r,y}? A ∩ I = {a,r}
  16. 16. UNDERSTANDING DISJOINT SETS … <ul><li>3 5 </li></ul><ul><li>7 9 </li></ul>U A <ul><li>4 </li></ul><ul><li>6 8 </li></ul>A = {1,3,5,7,9} B = {2,4,6,8} = { } or  A ∩ B B
  17. 17. DISJOINT SETS are sets having null or empty intersection. In other words, disjoint sets are sets without common element. REMEMBER: No elements are the same!
  18. 18. Which of the sets are disjoint ? O = {u,s,h,e,r} M = {j,u,s,t,i,n} G = {l,a,d,y,g} O and G M and G
  19. 19. UNDERSTANDING CARTESIAN PRODUCT … A = {a,b} B = {1,2,3} ={(a,1),(a,2),(a,3),(b,1),(b,2),(b,3) } A x B ={(1,a),(1,b),(2,a),(2,b),(3,a),(3,b) } B x A
  20. 20. CARTESIAN PRODUCT is a set consisting of all the pairs of the elements of set A to set B. This is denoted by x. A x B is read as “A cross B” REMEMBER: Elements in Cartesian Product should be PAIRS!
  21. 21. What are the Cartesian Products of A cross B? A = {spongebob,patrick} B = {sandy,squidward} A x B = {(spongebob,sandy), (sponebob,squidward), (patrick,sandy), (patrick,squidward)}
  22. 22. WE DID IT! Hurray!

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