KALKULUS (HIMPUNAN)

Misalkan :               S = {x │ x bilangan bulat positif, x ≤ 10}

                                P = {1, 2, 3, 7}

                                Q = {2, 4, 6, 9}

                                R = {1, 3, 5, 8}

(P U Q) ∩ (P’ ∩ R)’        = P U (Q’ U R)’

P U Q                              = {1, 2, 3, 7} U {2, 4, 6, 9}

                                        = {1, 2, 3, 4, 6, 7, 9}

P’                                     = {4, 5, 6, 8, 9, 10}

P’ ∩ R                             = {4, 5, 6, 8, 9, 10} ∩ {1, 3, 5, 8}

                                                = {5, 8}

(P’ ∩ R)’                         = {1, 2, 3, 4, 6, 7, 9, 10}

(P U Q) ∩ (P’ ∩ R)’        = {1, 2, 3, 4, 6, 7, 9} ∩ {1, 2, 3, 4, 6, 7, 9, 10}

                                        = {1, 2, 3, 4, 6, 7, 9}

Q’                                    = {1, 3, 5, 7, 8, 10}

Q’ U R                            = {1, 3, 5, 7, 8, 10} U {1, 3, 5, 8}

                                        = {1, 3, 5, 7, 8, 10}

(Q’ U R)’                        = {2, 4, 6, 9}

P U (Q’ U R)                  = {1, 2, 3, 7} U {2, 4, 6, 9}

                                       = {1, 2, 3, 4, 6, 7, 9}

(P U Q) ∩ (P’ ∩ R)’       = P U (Q’ U R)

{1, 2, 3, 4, 6, 7, 9}          = {1, 2, 3, 4, 6, 7, 9}

Jadi terbukti sama.