Your SlideShare is downloading. ×
0
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Concept of set.
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×
Saving this for later? Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime – even offline.
Text the download link to your phone
Standard text messaging rates apply

Concept of set.

4,454

Published on

chapter 2

chapter 2

0 Comments
3 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
4,454
On Slideshare
0
From Embeds
0
Number of Embeds
1
Actions
Shares
0
Downloads
0
Comments
0
Likes
3
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. CONCEPT OF SETS.
  • 2. 1.Way of listing the elements ofSets Put the elements in curly brackets.. {1,2,3,4}
  • 3. 2.Specifying properties of sets i) intensional definition A is the set whose members are the first four days in a week. ii) extensional definition A = {Sunday, Monday, Tuesday, Wednesday}
  • 4. 3.Set membership , ∈ ∈ means element of a.k.a relation x ∈ A means x is an element of set A A contains x A x
  • 5. 4.Empty set.. Empty set is a set having no elements.
  • 6. 5.Set of numbers (Z,N,etc....)
  • 7. 6.Set EqualityDefinition: Two sets are equal if and only if they have the same elements.Example:{1,2,3} = {3,1,2} = {1,2,1,3,2}Note: Duplicates dont contribute anything new to aset, so remove them. The order of the elements in aset doesnt contribute anything new. Example: Are {1,2,3,4} and {1,2,2,4} equal?No!
  • 8. 8.Subset Definition: A set A is said to be a subset of B if and only if every element of A is also element of B. We use A ⊆ B to indicate A is a subset of B. Example: A={1,2,3} B ={1,2,3,4,5} Is: A ⊆ B ? Yes.
  • 9. POWER SET Power set of S is the set of all subsets of the set S. The power of set S is denoted by P(S). Example: What is the power set of set {3, 4, 5} ?Solution:P({3, 4, 5}) is the set of all subsets of {3, 4, 5}P({3, 4, 5}) = {Ø, {3}, {4}, {5}, {3, 4}, {3, 5}, {4, 5}, {3, 4, 5}.
  • 10. SET OPERATIONUnionA∪BBoth circle are shaded.
  • 11. SET OPERATIONIntersectionA∩BOnly the portion shared by both circles are shaded.
  • 12. OPERATION SET Disjoint setIf the intersection is empty, we called disjoint set. U A B
  • 13. OPERATION SETSet differenceA-B
  • 14. OPERATION SETExample set difference :K = {a, b} L = {c, d} M = {b, d}K –L ={a, b}K –M ={a}L – M= {c}K–K=ØK–Ø=KØ–K=Ø
  • 15. OPERATION SETSet complimentaryEverything in universe that is not in the set
  • 16. OPERATION SET Example : U={A,B,C,D,E,F,G} C={A,B,D,E,F} C´={C,G} U-C=C´
  • 17. OPERATION SETCharacteristics of set.
  • 18. GENERELISE UNION ANDINTERSECTION
  • 19. GENERELISE UNION ANDINTERSECTIONExample :Let A ={0,2,4,6,8}, B ={0,1,2,3,4} and C ={ 0,3,4,9}.A∪B ∪C :{0, 1 ,2, 3, 4, 6, 7, 8, 9}A ∩ B∩ C :{0}
  • 20. CARTESIAN PRODUCT A and B are set A and B is set of all ordered pairs(a,b) where A∈a and b∈BExample:Suppose A={1,2,} and B={2,3}. ThenA×B={(1,2),(1,3),(2,2),(2,3) }andB×A={(2,1),(2,2),(3,1),(3,2)}

×