Agenda, Semester Week 1

Agenda, Semester Week 1#

Propositional Logic#

The first week of the course is dedicated to an introduction to propositional logic. Propositional logic is an important and fundamental branch of mathematics that constitutes a cornerstone for how mathematical statements - propositions - are formulated and for how mathematical arguments are presented.

Remark#

Prior to week 1, please familiarize yourself with the course structure by looking through the pages of this website. In the course’s DTU Learn module you can check which group you are assigned to. Look out for a welcome message from your group’s TA’s who will welcome you at the exercise session on the first day.

Key Terms#

Long Day will cover:

  • Propositions, truth values and truth tables.

  • Logical operations: conjunction \(\land\), disjunction \(\lor\), negation \(\lnot\).

  • Implication \(\Rightarrow\) and biimplication \(\Leftrightarrow\).

  • Logical consequence and logical equivalence.

  • Tautologies \(\mathbf T\) and contradictions/falsehoods \(\mathbf F\).

Short Day will cover:

  • Proof by contradiction and proof by contrapositive.

  • The transition from logics to mathematics.

Preparation and Syllabus#

Syllabus this week is Chapter 1.

  • For Long Day, read Sections 1.1, 1.2, 1.3 and 1.5.

  • For Short Day, read Section 1.4 and review Section 1.3 from Theorem 1.3.4 onward.

Recommended approach: Read or skim the material before a lesson. After lectures and exercises, do an in-depth re-read of the material. Material of future weeks will rely on that of earlier weeks, so make sure you master the week’s material before the week ends.

The textbook can be found in an electronic version on this website, and can also be purchased in a physical form in the DTU Polyteknisk bookstore. For the exam you cannot bring the electronic version, so it is recommended that you acquire it in physical form.

Exercises#

Exercises for Long Day.

Exercises for Short Day.

Contents