Diskretne strukture
Osnutek odseka
-
Predavanja:
Matematična indukcija.Izjave, izjavni vezniki. Izjavni izrazi, resničnostna tabela, enakovredni izjavni izrazi. Zakoni izjavnega računa.Lectures:
Mathematical induction (pages 5-7);Introduction into propositional logic: atoms, logical connectives, logical formulas, truth tables, equivalence of formulas (pages 95-99). Laws of propositional logic (pages 11-15). -
-
Predavanja: DNO in KNO. Polni nabori izjavnih veznikov. Sklepanje v izjavnem računu. Formalizacija sklepov.
Lectures: Disjunctive and conjuctive normal form (pages 4-6); Functionally complete sets of connectives. Logical inference - formalization, rules of inferece,
-
Predavanja: Sklepanje v izjavnem računu. Formalizacija sklepov, definicija pravilnega sklepa, pravila sklepanja, dokaz pravilnosti sklepa. Pomožni sklepi - pogojni sklep, sklep s protislovjem, analiza primerov.
Predikatni račun - jezik predikatnega računa, formalizacija, interpretacija.
Lectures: Logical inference - formalization, rules of inferece, derivation of rules (pages 100-104). Proof by contradiction (section 8 - on this link you can freely download the book), proof by conditional derivation (section 6.2), proof by cases (explained at the bottom of section 3.2).
Predicate calculus - language, formalization, interpretation.
-
-
Predikatni račun - jezik predikatnega računa, izjavne formule. Doseg kvantifikatorjev, proste in vezane spremenljivke. Interpretacija izjavne formule, enakovrednost izjavnih formul, preimenovanje spremenljivk, zakoni predikatnega računa,
Predicate logic: predicates; universe of discourse, universal and existential quantifier. (link) Scope of quantifiers. Free and bound variables. Well-formed formulas. Interpretation of formulas, equivalence of formulas. Laws of predicate calculus.
-
Preneksna normalna oblika izjavne formule.
Množice, osnovne operacije z množicami, lastnosti komplementiranja, osnovne enakosti množic. Potenčna množica. Družine množic.
Prenex normal form.
Sets, basic operations with sets, laws for operations with sets. (notes, on this link there are some proofs of laws of set theory). Power set. Families of sets.
-
-
Kartezični produkt.
Moč končnih množic.
Definicija relacije, lastnosti relacij.
Cartesian product.
Cardinality of finite sets.
Relations, definition and examples, properties of relations (link),