Logic and Sets

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.

TYPE OF ASSESSMENT
A written midterm exam (40% of the grade) and a written final exam (60% of the grade).

For both the midterm and the final exam, at least a 5.0 must be achieved. (And the overall mark must be at least 5.5.)

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.