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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 )

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CHAPTER (6)

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  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

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