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## Logic and Sets

2019-2020

### Course Objective

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

### Course Content

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.

### Teaching Methods

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.

### Method of Assessment

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

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.

### Literature

All course materials will be provided via Canvas.

1CS, 1LI, 1IMM

### General Information

Course Code X_401090 6 EC P4 100 English Faculty of Science prof. dr. W.J. Fokkink prof. dr. W.J. Fokkink prof. dr. W.J. Fokkink dr. W. Kager

### Practical Information

You need to register for this course yourself

Last-minute registration is available for this course.

Teaching Methods Lecture, Seminar*

*You cannot select a group yourself for this teaching method, you will be placed in a group.

Target audiences

This course is also available as: