URL study guide
https://tue.osiris-student.nl/onderwijscatalogus/extern/cursus?cursuscode=2IT60&collegejaar=2025&taal=enDescription
Subjects: Propositions, truth tables, equivalence, logical consequence, tautology,contradiction, contingency. Predicates, quantifiers, 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, equivalence class.
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.
Induction, strong induction, inductive definition.
Objectives
After completing the course, the student1. can formalise first-order properties with formulas of predicate logic;
2. can prove that a first-order formula of predicate logic is a tautology using a natural-deduction style formal system;
3. can reproduce the formal definitions of predicates and operations on sets (set comprehension, subset, intersection, union, complement, set difference, empty set, power set, Cartesian product);
4. can reproduce the formal definitions pertaining to relations (equivalence relation, equivalence class, composition of relations);
5. can reproduce the formal definitions pertaining to mappings (image and source, injection, surjection, bijection, inverse mapping, composition of mappings);
6. can prove simple first-order properties about sets, relations and functions using generally accepted mathematical proof techniques (e.g., direct proof, contradiction, case distinction) ;
7. can refute the validity of a first-order property about sets, relations and functions with a counterexample;
8. can reproduce the formal definitions pertaining to partial orderings (linear partial ordering, minimal and maximal elements, minimum and maximum);
9. has a systematic approach (in particular, can systematically draw conclusions according to a predefined collection of axioms and inference rules);
10. can prove properties with induction.