Unformatted text preview: inverse of R , written R1 , is deFned by a R1 b if and only if b R a . Inverse should not be confused with complement: for example, the inverse of ‘is a parent of’ is ‘is the child of’; if z is the cousin of y , then z is in the complement of ‘is a parent of’, but not the inverse. Using the R from example 3.5, the inverse R1 = { (2 , 1) , (3 , 2) , (4 , 3) , (1 , 4) } . If we take the inverse of the inverse of a relation, we recover the original relation: ( R1 )1 = R . D EFINITION 3.8 (C OMPOSITION OF R ELATIONS ) Given R ⊆ A × B and S ⊆ B × C , then the composition of R with S , written R ◦ S , is deFned by a R ◦ S c if and only if ∃ b ∈ B. ( a R b ∧ b S c ) 19...
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 Spring '09
 Koskesh
 Math, Set Theory, relation, Composition of relations, Inverse relation, E R S E R E L

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