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CSE 2353 – September 25 th 2002

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CSE 2353 – September 25th 2002

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}

- X-Y Plot
- Two Lines
- Dia-graph
- “Adjacency” Matrix

- 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 aA
- Symmetric iff aRb -> bRa for all a,bA
- Anti-symmetric iff aRb and bRa -> a=b for all a,bA
- Transitive iff aRb and bRc -> aRc
- Example: R is a relation on the real numbers: xRy iff x y