Tugas himpunan

Tugas Himpunan 1

Jika P,Q,R adalah himpunan ,buktikan bahwa

(PᴗQ)ᴖ(P^cᴖR)^c = Pᴗ(Q^cᴗR)^c

Pembuktian

Pembuktian 1

Diketahui :

P={1,3,4,6,7}                      S={1,2,3,4,5,6,7,8,10,11,13}

Q={2,3,4,5,8,10}               

R={1,6,10,11,13}

Jawab :

PᴗQ                       ={1,2,3,4,5,6,7,8,9,10}                    Q^C                           ={1,6,7,11,13}

P^C                                          ={1,2,3,4,5,6,7,8}                              Q^CᴗR                      ={1,6,7,10,11,13}

P^CᴖR                      ={10,11,13}                                         (Q^CᴗR)^C                         ={2,3,4,5,8}

(P^CᴖR)^C                 ={1,2,3,4,5,6,7,8}                             

(PᴗQ)ᴖ(P^CᴖR)^C            ={1,2,3,4,5,6,7,8}                    Pᴗ(Q^CᴗR)^C               ={1,2,3,4,5,6,7,8}

Pembuktian 2

Diketahui :

P={a,b,d,h,i,k}                   S={a,b,c,d,e,f,g,h,i,j,k}

Q={b,c,e,f,h}

R={c,d,g,h,j}

Jawab :

PᴗQ                       ={a,b,c,d,e,f,h,i,k}                                           Q^c                                         ={a,d,g,i,j,k}      

P^c                                          ={c,f,g,j}                                                               Q^cᴗR                      ={a,c,d,g,h,I,j,k}

P^cᴖR                       ={c,g,j}                                                                  (Q^cᴗR)^c                          ={b,e,f}

(P^cᴖR)^c                           ={a,b,d,e,f,h,i,k}                                                              

 (PᴗQ)ᴖ(P^cᴖR)^c    ={a,b,d,e,f,h,i,k}                                                              Pᴗ(Q^cᴗR)^c                  ={a,b,d,e,f,h,I,k}