Matematična logika in logične naloge

Abstract

Keywords

Data

Language:	Slovenian
Year of publishing:	2013
Source:	Ljubljana
Typology:	2.11 - Undergraduate Thesis
Organization:	UL PEF - Faculty of Education
Publisher:	[K. Zupančič]
UDC:	510.6(043.2)
COBISS:	9797449
Views:	1071
Downloads:	202
Average score:	0 (0 votes)
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Secondary language:	English
Secondary title:	Mathematical logic and logical puzzles
Secondary abstract:	In this BSc thesis entitled Mathematical logic and logical puzzles we introduce some basics concerning the theory of mathematical logic, strategies for solving logical problems and examples of such problems that occur in logic competitions in primary and secondary schools. In the first part we introduce the basics of mathematical logic required for the understanding and successful solving of logical problems. Firstly we introduce the objects with which we work. These are propositions and propositional conjunctions. Next we study the relations between them, introduce the concept of equivalence of propositions, the selected forms of propositions, the full collection of conjunctions and the logical implications. At the end we use all this knowledge in the propositional calculus. What follows is a short introduction into set theory that is needed in an important part of mathematical logic--predicate calculus. In the second part of this thesis we establish different ways of proving the truthness or falseness of propositions. We consider an effective, universal method for solving mathematical logical problems which may be helpful in solving any mathematical problem. In the last part of this thesis we make a brief summary of logical problems that occur in Slovene logic competitions organised by the Slovene technical culture association (ZOTKS). At the end we provide examples of different types of such problems and solve some of them step by step.
Secondary keywords:	logic;logika;
File type:	application/pdf
Type (COBISS):	Bachelor thesis/paper
Thesis comment:	Univ. Ljubljana, Pedagoška fak., Matematika-računalništvo
Pages:	44 str.
Type (ePrints):	thesis
Title (ePrints):	Mathematical logic and logical puzzles
Keywords (ePrints):	matematična logika
Keywords (ePrints, secondary language):	mathematical logic
Abstract (ePrints):	V diplomskem delu Matematična logika in logične naloge predstavimo nekaj osnov teorije matematične logike, strategije reševanja logičnih nalog in primere nalog, ki se pojavljajo na logičnih tekmovanjih v osnovni in srednji šoli. V prvem delu predstavimo osnove matematične logike, ki so potrebne za razumevanje in uspešno reševanja logičnih nalog. Najprej spoznamo objekte, s katerimi operiramo. To so izjave in izjavni vezniki. V nadaljevanju preučimo odnose med njimi, se seznanimo s pojmom enakovrednosti izjav, izbranimi oblikami izjav, polnimi nabori veznikov ter logičnimi posledicami, na koncu pa vse to povežemo in uporabimo pri sklepanju v izjavnem računu. Sledi krajši uvod v osnove teorije množic, ki jih potrebujemo za razlago pomembnega dela matematične logike-predikatnega računa. V drugem delu diplomskega dela spoznamo načine dokazovanja resničnosti ali neresničnosti izjav. Seznanimo se z učinkovito univerzalno metodo reševanja matematičnih logičnih nalog, ki nam lahko pomaga pri uspešnem reševanju poljubnega matematičnega problema. V zadnjem delu diplomskega dela naredimo kratek pregled logičnih nalog, ki se pojavljajo na slovenskem tekmovanju v logiki, ki jih organizira Zveza za tehnično kulturo Slovenije. Za konec nekatere po korakih rešimo.
Abstract (ePrints, secondary language):	In this BSc thesis entitled Mathematical logic and logical puzzles we introduce some basics concerning the theory of mathematical logic, strategies for solving logical problems and examples of such problems that occur in logic competitions in primary and secondary schools. In the first part we introduce the basics of mathematical logic required for the understanding and successful solving of logical problems. Firstly we introduce the objects with which we work. These are propositions and propositional conjunctions. Next we study the relations between them, introduce the concept of equivalence of propositions, the selected forms of propositions, the full collection of conjunctions and the logical implications. At the end we use all this knowledge in the propositional calculus. What follows is a short introduction into set theory that is needed in an important part of mathematical logic--predicate calculus. In the second part of this thesis we establish different ways of proving the truthness or falseness of propositions. We consider an effective, universal method for solving mathematical logical problems which may be helpful in solving any mathematical problem. In the last part of this thesis we make a brief summary of logical problems that occur in Slovene logic competitions organised by the Slovene technical culture association (ZOTKS). At the end we provide examples of different types of such problems and solve some of them step by step.
Keywords (ePrints, secondary language):	mathematical logic
ID:	8311758