SETS_relations

# SETS_relations - T ran S ∩ T ⊆ ran S ∩ ran T Inverse...

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Summary of Relations Domain dom( R ) = { x | ∃ y ( x, y ) R } Range ran( R ) = { y | ∃ x ( x, y ) R } Inverse R = { ( b, a ) • | ( a, b ) R } Identity id( A ) = { ( a, a ) | a A } Iteration R 0 = id( A ) R n = R ; R n - 1 Domain Restriction S / R = { ( a, b ) • | ( a, b ) R a S } Range Restriction R . S = { ( a, b ) • | ( a, b ) R b S } Relational Composition R ; S = { ( a, c ) • | ∃ b ( a, b ) R ( b, c ) S } Domain Properties dom( S ) A dom( S T ) = dom( S ) dom( T ) dom( S T ) dom( S ) dom( T ) Range Properties ran( S ) B ran( S T ) = ran( S ) ran(
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Unformatted text preview: T ) ran( S ∩ T ) ⊆ ran( S ) ∩ ran( T ) Inverse Properties ( R ∼ ) ∼ = R dom( R ∼ ) = ran( R ) ran( R ∼ ) = dom( R ) Iteration Properties R m + n = R m ; R n R m × n = ( R m ) n Relational Composition Properties R ; ( S ; T ) = ( R ; S ); T ( R ; S ) ∼ = S ∼ ; R ∼ id( A ); R = R R ; id( B ) = R...
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