Дискретная математика. Множества. Отображения. Отношения

84 Q ∩ R = { ( a 1 , b 1 ), ( a 3 , b 2 ) } ; [ Q ∩ R ] = 1 0 0 0 1 0 1 1 1 0 0 0 0 0 0 0 0 1 0 0 & 1 0 0 1 0 1 0 0 1 1 0 0 0 1 1 0             =                   = [ Q ] & [ R ]; { } 1 2 1 3 1 4 2 2 2 3 3 1 3 4 ( , ), ( , ), ( , ), ( , ), ( , ), ( , ), ( , ) R a b a b a b a b a b a b a b = ; 0 1 1 1 1 0 0 0 0 1 1 0 1 0 0 1 [ ] 1 [ ] 1 0 0 1 0 1 1 0 R R R           = = ¬ = ¬ = −               ; { } 1 3 1 4 2 2 3 1 \ ( , ), ( , ), ( , ), ( , ) Q R a b a b a b a b = ; [ Q \ R ] = 0 0 1 1 1 0 1 1 0 1 1 1 0 1 0 0 0 1 0 0 & 0 1 1 0 1 0 0 0 1 1 0 0 1 0 0 1             =                   = [ Q ]&(1 – [ R ]); { } 1 1 1 3 1 4 1 2 2 1 3 2 3 ( , ), ( , ), ( , ), ( , ), ( , ), ( , ) Q a b a b a b a b a b a b − = ; [ Q –1 ] = 1 0 1 0 1 1 1 0 0 1 0 0              = 1 0 1 1 0 1 0 0 1 1 0 0 T           = [ Q ] T . Отношение тождества 2 A A θ ⊂ на множестве A равно A θ = 1 1 2 2 3 3 {( , ), ( , ), ( , )} a a a a a a = и матрица этого отношения [ ] A θ = 1 0 0 0 1 0 0 0 1           = E 3