Discrete mathematics, Study notes of Discrete Mathematics

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Tabel Kebenaran P| a| p®q Pl) a|Ppaq P) a|PYq P od ©| TF) T| T| T | Z| 3 T|F c EF 1 T| F| F T) F| T B\t F| T| F F| T| T FF) T| T Fi Fi F ¥F| Fi F F F F 1. Hukum identitas: 2. Hukum null/dominasi: — pvFeop paForF Enters net 7, Hukum komutatif: 8, Hukum asosiatif: 3. Hukum negasi: 4, Hukum idempoten: - pyasaqvp - PYQavnsbvayr pype&®r Pypop - paqoqnp - PAGANS (Agar paper PApSp Vika” ca 9, Hukum disiributif: 10. Hukum De Morgan: a ao - pYGanerva@rpryn Mpage~py~q = epee - pv@Agep PAGVINSRAQv ar) ~ “pv g)o~pa-qg - PA@YQ)epP Cara-cara mengekspresikan implikasi p—> q° © Jika p, maka q (ifp, then q) © Jikap,q (ifp.@ © pmengakibatkang —— (p implies q) © qiikap (itp) © phanyajikaq (p only if q) © psyarat cukup untuk q_(p is sufficient condition for q) qsyarat perlu bagi p (qs necessary condition for p) © qbilamana p (q whenever p) © qmengikuti dari p (q follows from p) ACBS Vx (xeA > xeB) 428 & ACBdanBCA Notasi : A~ B <9|Aj = |B) Himpunan Kuasa * Notasi: P(A) atau 2° * Jika |A| =m, maka |P(A)| =2™. Operasi Terhadap Himpunan ~isan (intersection) 2. Gabungan (uion) © Notasi: 4 B= {x|xeAdanxe B} e Notasi: 4 B= {x|x € A ataux 3. Komplemen (complement) 4. Selisih (difference) ¢ Notasi: 4={x|xeU,xe@Ad © Notasi:4-B={x|xeAdanxe B}= ANB 5. Beda Setangkup (Symmetric Difference) * Notasi: 4 ® B= (4 U B)—- (44 B)=(A-B) VU (B-A) 6. Perkalian Kartesian (cartesian product) . Notasi: A x B= {(a,b) | ae Adanbe B}