Logic and Sets

2019-2020
Dit vak wordt in het Engels aangeboden. Omschrijvingen kunnen daardoor mogelijk alleen in het Engels worden weergegeven.

Doel vak

After completing this course, the student can
1. express logical statements in propositional and predicate logic
2. reason about the meaning of such formulas through truth tables and
models
3. argue formally whether one formula implies another one, or that they
are equivalent
4 reduce a propositional formula to disjunctive or conjunctive normal
form
5. express propositional formulas in logic circuits and OBDDs

Furthermore, the student is able to
6. reason about set constructions through Venn diagrams and the algebra
of sets
7. construct and interpret formal, graphic, and matrix representations
of sets, relations and functions
8. determine and argue whether
a. a relation is reflexive, transitive, symmetric or antisymmetric
b. a relation is an ordering relation, equivalence relation, or a
function
c. a function is injective or surjective
9. construct and interpret compositions of relations (or functions) and
their inverses
10. construct a proof by mathematical induction

Inhoud vak

The sets part of the course starts by introducing the concepts of
sets, Venn diagrams, product sets and relations. The student then
learns the main characteristics and properties of three particular
types of relation: ordering relations, equivalence relations and
functions. The sets part concludes with a study of the principle of
mathematical induction.

The logic part focuses in the first place on propositional logic: truth
tables, boolean operators, functional completeness, logical puzzles,
SAT-solving, logic circuits and OBDDs. In addition the student will
learn the meaning and use formulas of predicate logic, to express
mathematical properties and sentences from natural language.

Onderwijsvorm

Every week, there is one 2-hour lecture and one 2-hour tutorial for
the logic part of the course, and one 2-hour lecture and one 2-hour
tutorial for the sets part of the course.

Toetsvorm

One written midterm exam (50% of the grade) and a written final
exam (50% of the grade).

The resit exam covers all material of the course. It is not possible to
resit only the midterm exam or only the final exam of the course.

Literatuur

All course materials will be provided via Canvas.

Doelgroep

1CS, 1LI, 1IMM

Algemene informatie

Vakcode X_401090
Studiepunten 6 EC
Periode P4
Vakniveau 100
Onderwijstaal Engels
Faculteit Faculteit der Bètawetenschappen
Vakcoördinator prof. dr. W.J. Fokkink
Examinator prof. dr. W.J. Fokkink
Docenten prof. dr. W.J. Fokkink
dr. W. Kager

Praktische informatie

Voor dit vak moet je zelf intekenen.

Voor dit vak kun je last-minute intekenen.

Werkvormen Deeltoets extra zaalcapaciteit, Hoorcollege, Werkcollege*

*Voor deze werkvorm kun je geen groep kiezen, je wordt hiervoor ingedeeld.