Logic and Sets

 
Course code:
X_401090
Period:
Period 4
Credits:
6.0
Language of tuition:
English
Faculty:
Faculty of Science
Coordinator:
prof. dr. W.J. Fokkink
Examinator:
prof. dr. W.J. Fokkink
Lecturers:
prof. dr. W.J. Fokkink
dr. W. Kager
Teaching method(s):
Lecture, Seminar,
Level:
100

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
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. use the algebra of sets to prove that two sets are equal
7. draw graphic and matrix representations of sets, relations and
functions
8. use such representations and (formal) reasoning to
a. determine properties of sets, relations and functions
b. determine and show whether a relation is an ordering relation,
equivalence relation or a function
c. determine the result of operations on sets, relations and functions
9. express a relation (function) in terms of given relations (functions)
by
means of the fundamental operations on relations (functions)
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.

Form of tuition

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.

Type of assessment

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.

Course reading

All course materials will be provided via Canvas.

Target audience

1CS, 1LI, 1IMM

© Copyright VU University Amsterdam
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