Hasyim Saripudin: himpunan

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}

Hasyim Saripudin