1 / 15

CHAPTER (6)

CHAPTER (6). RELATIONS. RELATIONS : - Let A and B be sets . A binary relation from A to B is subset of A* B …. EXAMPLE : Let A be the set of student in your school and let B be the set of courses , let R be the relation that consists of those pairs ( a,b )

zinnia
Download Presentation

CHAPTER (6)

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. CHAPTER (6) RELATIONS

  2. RELATIONS : - Let A and B be sets . A binary relation from A to B is subset of A* B …

  3. EXAMPLE : Let A be the set of student in your school and let B be the set of courses , let R be the relation that consists of those pairs (a,b) A) Fine the pair from this relation B) The pair (arabic ,haya)relation from(a,b) !? Solution : (1) (MONA,ENGLISH) .. (2) (ARABIC ,HAYA) is not in R ..

  4. INVERSE Relation : Let R be any relation from a set A to set B , R=(a,b) , R=(b,a)The inverse of R denoted by R -1 -1

  5. EXAMPLE : LetA = [1,2,3] and B=[x,y,z] Fine the inverse relation … Solution : ]R=[ (1,y),(1,z),(3,y) R=[ (y,1),(z,1),(y,3) ] Directed graphs of relation on sets -1

  6. EXAMPLE : Draw the directed graph of relation on the set : A=[1,2,3] (Fine 7 pairs) Solution : R=[(1,2),(2,2),(2,4),(3,2),(3,4),(4,1),(4,3)] 1 2 3 4

  7. PICTURES OF RELATIONS SETS :’’ Suppose A and B are set , there are two ways of picturing A relation R from A to B 1) Matrix of the relation 2) Arrow diagram

  8. EXAMPLE : Let A=[1,2,3] AND B=[x,y,z] Fine A R B and draw pictures of it (fine 3 pairs) Solution : R=[(1,y),(1,z),(3,y)] Picture of R

  9. MATRIX OF R 1 2 3 X Y Z ARROW OF DIAGRAM

  10. TYPE OF RELATIONS : 1- REFLIXUE : X R X 2- SYMMETRIC : a R b b R a 3- anti-symmetric : arb ^ brc a=b 4- transitive : a R b ^ b R a a R b

  11. EXAMPLE : • Given X breather of Y , C breather of Y , • WHAT IS THE TYPE OF THIS RELATION ? • Solution : • X breather Y • Y breather C • Then C breather X this transitive relation

  12. EXAMPLE : Given A=[1,2,3] AND B =[1,2] , R=[(2,1),(3,1),(3,2)] FINE MATRIX FOR R .. Solution : MR = 0 0 1 0 1 1

  13. EXAMPLE : Let A=[a1,a2,a3] and B=[b1,b2,b3,bn,b5] Which order pairs are in the relation R represent By matrix Mr = 0 1 0 0 0 1 0 1 1 0 1 0 1 0 1

  14. Solution : R=[(A1,B2),(A2,B1),(A2,B3),(A2,B4),(A3,B1),(A3,B3),(A3,B5)]

  15. THANKS FOR ALL

More Related