Post on 14-Dec-2015
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Any question ?
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
cartesianproduct
A = {a, b, c} B = {sm*sh, cherrybelle, JKT48} AxB = {(a,sm*sh), (a,cherrybelle), (a,JKT48),
(b,sm*sh), (b,cherrybelle), (b,JKT48),
(c,sm*sh), (c,cherrybelle), (c,JKT48)}
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Super Junior
Cherrybelle
SM*SH
AKB48
A B
cartesianproduct berlaku?
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Super Junior
Cherrybelle
SM*SH
AKB48
A B
ℛ = {(Morgan, SM*SH), (Annisa, Cherrybelle), (Sashihara Rino, AKB48), (Ye Sung, Super Junior)}
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Super Junior
Cherrybelle
SM*SH
AKB48
A B
a ℛ b
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Super Junior
Cherrybelle
SM*SH
AKB48
A B
(a, b) ∈ ℛ
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Super Junior
Cherrybelle
SM*SH
AKB48
A B
Domain coDomain/range
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Super Junior
Cherrybelle
SM*SH
AKB48
A B
ℛ ⊆ (A x B)
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
A BMorgan SM*SHAnnisa Cherrybelle
Sashihara Rino AKB48Ye Sung Super Junior
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
0 0 1 00 1 0 00 0 0 11 0 0 0
Morgan
Annisa
Sashihara Rino
Ye Sung
Super
Junior
Cherry
belle
SM
*SH
AK
B48
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ℛ = {(a, a), (a, b), (b, a), (b, c), (b, d), (c, a), (c, d), (d, b)}
ℛ adalah relasi dari {a, b, c, d}
ab
cd
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ℛ = {(a, a), (a, b), (b, a), (b, c), (b, d), (c, a), (c, d), (d, b)}
ℛ adalah relasi dari {a, b, c, d}
ab
cd
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ℛ = {(a, a), (a, b), (b, a), (b, c), (b, d), (c, a), (c, d), (d, b)}
ℛ adalah relasi dari {a, b, c, d}
ab
cd
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ℛ = {(a, a), (a, b), (b, a), (b, c), (b, d), (c, a), (c, d), (d, b)}
ℛ adalah relasi dari {a, b, c, d}
ab
cd
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ℛ = {(a, a), (a, b), (b, a), (b, c), (b, d), (c, a), (c, d), (d, b)}
ℛ adalah relasi dari {a, b, c, d}
ab
cd
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ℛ = {(a, a), (a, b), (b, a), (b, c), (b, d), (c, a), (c, d), (d, b)}
ℛ adalah relasi dari {a, b, c, d}
ab
cd
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ℛ = {(a, a), (a, b), (b, a), (b, c), (b, d), (c, a), (c, d), (d, b)}
ℛ adalah relasi dari {a, b, c, d}
ab
cd
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ℛ = {(a, a), (a, b), (b, a), (b, c), (b, d), (c, a), (c, d), (d, b)}
ℛ adalah relasi dari {a, b, c, d}
ab
cd
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ℛ = {(a, a), (a, b), (b, a), (b, c), (b, d), (c, a), (c, d), (d, b)}
ℛ adalah relasi dari {a, b, c, d}
ab
cd
20
P = {2, 3, 4} Q = {2, 4, 8, 9, 15}
(p, q) ∈ ℛ jika p habis membagi q
21
P = {2, 3, 4} Q = {2, 4, 8, 9, 15}
(q, p) ∈ S jika q kelipatan p
22
P = {2, 3, 4} Q = {2, 4, 8, 9, 15}
(q, p) ∈ ℛ-1
jika q kelipatan p
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Bisma
Super Junior
Cherrybelle
SM*SH
AKB48
A BIndonesia
Korea
Jepang
Cℛ S
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Bisma
Super Junior
Cherrybelle
SM*SH
AKB48
A BIndonesia
Korea
Jepang
Cℛ S
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Bisma
Super Junior
Cherrybelle
SM*SH
AKB48
A BIndonesia
Korea
Jepang
Cℛ S
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Bisma
Super Junior
Cherrybelle
SM*SH
AKB48
A BIndonesia
Korea
Jepang
Cℛ S
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Bisma
Super Junior
Cherrybelle
SM*SH
AKB48
A BIndonesia
Korea
Jepang
Cℛ S
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
Morgan
Annisa
Sashihara Rino
Ye Sung
Bisma
Super Junior
Cherrybelle
SM*SH
AKB48
A BIndonesia
Korea
Jepang
Cℛ S
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
S o ℛ = {(Morgan, Indonesia), (Annisa, Indonesia), (Sashihara
Rino, Jepang), (Ye Sung, Korea), (Bisma, Indonesia)}
a ℛ b; b S c
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
ab
cd
Equivalent Relation
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
NIM Nama Matakuliah Nilai
101 Wibisono Mat.Diskrit C
101 Wibisono StrukDat D+
102 Sukmo Mat.Diskrit A
102 Sukmo StrukDat B+
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
NIM
Nama
Matakuliah
Nilai
n-ary relation
Wibisono Sukmo Wardhono, ST, MThttp://wibiwardhono.lecture.ub.ac.id
NIM Nama
2-ary relationbinary relation