Kalkulus (Himpunan)

Pembuktian bahwa :

(P ᴗ Q) ᴖ (P’ ᴖ R)’ = P ᴗ (Q’ ᴗ R)’

Misal:

S = {1,2,3,4,5,6,7,8,9,10}

P = {2,4,6,7}                                        P’ = {1,3,5,8,9,10}

Q = {3,5,9,10}                                     Q’ = {1,2,4,6,7,8}

R = {1,5,6,7,8}

Diketahui:

(P ᴗ Q) = A’ = {2,3,4,5,6,7,9,10}

(P’ ᴖ R) = B = {1,5,8}                        B’ = (2,3,4,6,7,9,10}

(A ᴖ B’) = {2,3,46,7,9,10}

(Q’ ᴗ R) = C = {1,2,4,5,6,7,8}         C’ = {3,9,10}

(P ᴗ C’) = {2.3.4.6.7.9.10}

Jadi, benar bahwa (P ᴗ  Q) ᴖ  (P’ ᴖ R)’ = P ᴗ (Q’ ᴗ R)’