Di sebuah pulau terdapat dua golongan penduduk ksatria

Di sebuah pulau terdapat dua golongan penduduk - ksatria; yang selalu bicari jujur - penipu; yang selalu berbohong. Suatu hari, anda bertemu dengan dua orang, A dan B. A berkata “B adalah seorang ksatria” B berkata “Golongan kami berbeda” Termasuk golongan apa A dan B? Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

TIF 4216 Matematika Diskrit Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

Any question? Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

Rafael Morgan Rangga Dicky Ilham Reza Bisma Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

TEORI HIMPUNAN Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

HIMPUNAN oby ek oby ek Anggota/ Elemen/ Unsur oby ek Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

l. Listing Method A = {1, 2, 3, 4, 5, 6} l. Description Method l(notasi pembentuk himpunan) l. A = {x | 1 ≤ x ≤ 6 ; x bil. bulat} Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

Listing Method elemen A = {1, 2, 3, 4, 5, 6} Sedemikian hingga Description Method (notasi pembentuk himpunan) A = {x | 1 ≤ x ≤ 6 ; x bil. bulat} syarat Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

l. Listing Method A = {1, 2, 3, 4, 5, 6} l. Description Method l(notasi pembentuk himpunan) l. A = {x | 1 ≤ x ≤ 6 ; x bil. bulat} Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

A = {1, 2, 3, 4, 5, 6} 3 A 9 A Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

KARDINALITAS A = {1, 2, 3, 4, 5, 6} n(A) = 6 |A| = 6 Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

P = { x | x adalah mahasiswa kelas ini yang menjadi penggemar SM*SH } |P| = 0 P= P = {} Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

U JOHNVENN A 11 13 3 2 5 7 1 B 9 Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

U A B 1 A B 2 4 3 Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

Hubungan ANTAR-HIMPUNAN Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

HIMPUNAN BAGIAN Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

1. A A 2. A 3. A B B C A C Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

A B B A A=B Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

A = {1, 2, 3} C = {1, 2, 3, 4, 5} A B dan B C --> Proper Subset Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

U A Tama-Iim Dodhy. Andika Bebe-Izzy Ilham-Reza Bisma-Dicky. Morgan Rangga. Rafael B Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

HIMPUNAN SALING LEPAS vx A ≠ vx B U A || A B B Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

HIMPUNAN SALING BERPOTONGAN x A = x B U A B Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

OPERASI DASAR DALAM HIMPUNAN l. Operasi dasar himpunan: Gabungan (union); A B = {x | x A dan x B} - Irisan (intersection); A B = {x | x A atau x B} - Komplemen (complement); Ac = {x | x S; x A} c Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

A B = B A ; Hukum komutatif bagi gabungan 2. A B = B A ; Hukum komutatif bagi irisan 3. A (B C) = (A B) C ; Hukum asosiatif bagi gabungan 4. A (B C) = (A B) C ; Hukum asosiatif bagi irisan 5. A (B C) = (A B) (A C) ; Hukum distribusi bagi gabungan 6. A (B C) = (A B) (A C) ; Hukum distribusi bagi irisan 1. Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

1. Sc = 2. = S 3. (Ac)c = A 4. A Ac = S 5. A Ac = 6. (A B)c = Ac Bc ; Hukum De Morgan 7. (A B)c = Ac Bc ; Hukum De Morgan Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id

B = {a, b, c, d, e} ; A = {1, 2, 3} A X B = {(1, a), (1, b), (1, c), (1, d), (1, e), (2, a), (2, b), (2, c), (2, d), (2, e), (3, a), (3, b), (3, c), (3, d), (3, e)} Misalkan ada sebuah relasi R = {(1, a), (1, b), (2, d), (2, e), (3, a), (3, b)} Maka R ⊆ (A X B) (1, a) ∈ R (1, c) ∉ R Wibisono Sukmo Wardhono, ST http: //wibiwardhono. lecture. ub. ac. id