TUGAS HIMPUNAN

NAMA KELOMPOK : FAISAL AKBAR ISLAM MULLOH

KELOMPOK 4

NPM : 33413110

TUGAS : KALKULUS ( HIMPUNAN )

SOAL
Buktikan jika
(P ᴗ Q) ᴖ (P' ᴖ R)' = P ᴗ (Q' ᴗ R)'
Misalkan :
S = {2,4,6,8,10,12,14,16,18,20}
P = {2,4,6,8,10}
P' = {12,14,16,18,20}
Q = {4,10,12,14,16}
Q'= {2,6,8,18,20}
R = {4,8,10,16,18,20}
R'= {2,6,12,14}
PEMBUKTIAN

JAWAB :
P' ᴖ R = {16,18,20}
(P' ᴖ R)' = {2,4,6,8,12,14}
(P ᴗ Q) ᴖ (P' ᴖ R)' = {2,4,6,8,10,12,14,16} ᴖ {2,4,6,8,12,14} = {2,4,6,8,12,14}

Q' ᴗ R = {2,4. 6 ,8,10,16,18,20}
(Q' ᴗ R)' = {12,14}
P ᴗ (Q' ᴗ R)' = {2,4,6,8,10} ᴗ {12,14}= {2,4,6,8,10,12,14}
Jadi benar bahwa (P ᴗ Q) ᴖ (P' ᴖ R)' = P ᴗ (Q' ᴗ R)'--------> {2,4,6,8,10,12,14}