S={1,2,3,4,5,6,7,8,9,10} A={1,3,5,9} B={2,3,4,5,7} C={4,5,6,8,9} Tentukanlah: A.(A irisanB)union C B.A irisa(B union C) C.(A irisanB)komplemen union (B irisanC)

Diketahui:
S = {1,2,3,4,5,6,7,8,9,10}
A= {1,3,5,9}
B = {2,3,4,5,7}
C= {4,5,6,8,9}

Ditanya:
a) (A n B) U C
b) A n ( B U C)
c) (A n B)^c U ( B n C)

Jawab
Konsep dasar:
Irisan = anggota yang sama pada himpunan A dan B.
Gabungan= gabungan setiap anggota A dan B

a) A n B = {3, 5}
(A n B) U C = {3,4,5,6,8,9}

b) B U C = {2,3,4,5,6,7,8,9}
A n (B U C) = {3,5,9}

c) (A n B)^c = {1,2,4,7,9}
B n C = {4,5}
(A n B) ^c U (B n C) = {1,2,4,5,7,9}