After completing the course, the student can work with formulas from propositional logic and predicate logic, and knows their meaning and use. In particular, the student can prove the validity of a logical formula in a formal deductive system with assumptions, inferences and conclusions. The student can put his logical knowledge to work, in particular to prove formulas of set theory, having developed both the skills and the understanding of the fundamental mathematical abstractions in the area of sets, including relations, functions, orderings and induction.
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The course treats the following topics:
- syntax and semantics of propositional logic, including truth tables, equivalence, tautology and contradiction, calculating with equivalences, strengthening and weakening of propositions;
- syntax and (informal) semantics of first-order predicate logic, including predicates, quantifiers, and variable binding;
- logical derivation, reasoning with propositions and predicates, conclusion, assumption, context, validity;
- set, subset, intersection and union, complement, difference, the empty set, powerset, cartesian product;
- relation, equivalence relation, class, partition;
- mapping (function), image and source, injection, surjection, bijection, inverse function, composition of relations and functions;
- partial ordering, linear ordering, Hasse diagram, maximal and minimal elements; and
- induction, strong induction, inductive definition
This homologation course is a self-study course given by the TU/e (TU/e course code 5LIQ0 TU/e lecturer is Bas Luttik). It is only accessible for master Embedded Systems students and with explicit approval of the programme mentor. You must have a TU/e account.
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