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15+Slides--Closures%2C+Functions

# 15+Slides--Closures%2C+Functions - CS103 HO#15...

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CS103 HO#15 Slides--Closures, Functions 4/13/11 1 Composition of Relations R A B Suppose R is a relation on A x B Composition of Relations S R A B C Suppose R is a relation on A x B and S is a relation on B x C . Composition of Relations S R A B C Suppose R is a relation on A x B and S is a relation on B x C . The composition of R and S , denoted S o R , is a relation on A x C given by: S o R = {( a , c ) A x C | b B (( a, b ) R ( b , c ) S) } c a b Composition of Relations S R A B C Suppose R is a relation on A x B and S is a relation on B x C . The composition of R and S , denoted S o R , is a relation on A x C given by: S o R = {( a , c ) A x C | b B (( a, b ) R ( b , c ) S) } c a b Composition of Relations S R A B C A C S o R Suppose R is a relation on A x B and S is a relation on B x C . The composition of R and S , denoted S o R , is a relation on A x C given by: S o R = {( a , c ) A x C | b B (( a, b ) R (b, c ) S) } Cronus Zeus Poseidon Apollo Asclepius Zeus Poseidon Cronus Apollo Asclepius R R Composition of a Relation with Itself

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CS103 HO#15 Slides--Closures, Functions 4/13/11 2 Composition of a Relation with Itself Cronus Zeus Poseidon Apollo Asclepius Zeus Poseidon Cronus Apollo Asclepius R R R o R R 2 Composition of a Relation with Itself Cronus Zeus Poseidon Apollo Asclepius Zeus Poseidon Cronus Apollo Asclepius R R R o R R 2 Composition of a Relation with Itself Cronus Zeus Poseidon Apollo Asclepius Zeus Poseidon Cronus Apollo Asclepius R R R o R R 2 R o R 2 R 3 R o ( R o R ) Composition of a Relation with Itself Cronus Zeus Poseidon Apollo Asclepius Zeus Poseidon Cronus Apollo Asclepius R R R o R R 2 R o R 2 R 3 R o ( R o R ) Composition of a Relation with Itself Cronus Zeus Poseidon Apollo Asclepius Zeus Poseidon Cronus Apollo Asclepius R R R o R R 2 Father Grandfather Great-Grandfather R o R 2 R 3 R o ( R o R ) Composition of a Relation with Itself Cronus Zeus Poseidon Apollo Asclepius 5 4 3 1 2 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 1 0 1 0 0 Boolean Matrix Multiplication "and" instead of multiplication "or" instead of addition 0 - - - - - - - - - - - - - - - - - - - - - - - - =