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CSE 2353 – September 25 th 2002 - PowerPoint PPT Presentation

CSE 2353 – September 25 th 2002. Relations. Set Partitions. Math Review. Hamming Distance Error Correction. Relations. A R B is a subset of A X B a  A is related to b  B iff (a,b)  R Example: A = B = {1,2,3,4,5,6}; R = {(a,b): a divides b}. Display of Relations. X-Y Plot

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CSE 2353 – September 25th 2002

Relations

Hamming DistanceError Correction

• A R B is a subset of A X B

• a  A is related to b  B iff (a,b)  R

• Example:

• A = B = {1,2,3,4,5,6};

• R = {(a,b): a divides b}

• X-Y Plot

• Two Lines

• Dia-graph

• Identity

• Universal

• Inverse

• n-Ary

• Reflexive (a R a)

• Symmetric

• Anti-Symmetric

• Transitive

• Properties of the relation:

• R  S

• R  S

• R and S are Reflexive

• R and S are Symmetric

• R and S are anti-symmetric

• R and S are Transitive

• What Properties?

• reflexive?

• anti-symmetric?

• symmetric?

• transitive?

• Congruence modulo n

• a-b = kn

• a R b iff a <= b

• a R b iff a < b

• Reflexive iff aRa for all aA

• Symmetric iff aRb -> bRa for all a,bA

• Anti-symmetric iff aRb and bRa -> a=b for all a,bA

• Transitive iff aRb and bRc -> aRc

• Example: R is a relation on the real numbers: xRy iff x  y