Pembuktian Rumus Kalkulus - Himpunan

Nama : Violita Elgiana

Kelas : 1ID10 

NPM : 39413162

Membuktikan P, Q,R adalah himpunan buktikan bahwa (P ᴜ Q) n (P` n R)` = P ᴜ (Q` ᴜ R)`.

Misal :

S = {1,4,7,10,13,16,19,22,25,28}

P = {4,10,16,22,28} => P` = {1,7,13,19,25}

Q = {1,4,7,25,28} => Q` = {10,13,16,19,25}

R = {1,10,22,25,28}

Pembuktian :

(P ᴜ Q) = {1,4,7,10,16,22,25,28}

(P` n R) = {1,25}

(P` n R)` = {4,7,10,13,16,19,22,28}

• (P ᴜ Q) n (P` n R)`

=  {1,4,7,10,16,22,25,28} n {4,7,10,13,16,19,22,28}

= {4,7,10,16,22,28}

P = {4,10,16,22,28}

(Q` ᴜ R) = {1,10,13,16,19,22,25,28}

(Q` ᴜ R)` = {4,7}

• P ᴜ (Q` ᴜ R)`

=  {4,10,16,22,28} ᴜ {4,7}

= {4,7,10,16,22,28}

Kesimpulan :

Jadi, benar bahwa (P ᴜ Q) n (P` n R)` = P ᴜ (Q` ᴜ R)`.