# Introduction to Logic and Elementary Mathematics

## Objectives

Use of logical operations on propositions, conditions and sets to decide if a proposition is true or false and to prove theorems.

Use of elementary concepts of Set Theory, namely basic set operations, equivalence relations and order relations.

In learning process, logical reasoning and critical mind should be developed.

## General characterization

##### Code

10971

##### Credits

9.0

##### Responsible teacher

Júlia Maria Nunes Loureiro Vaz de Carvalho

##### Hours

Weekly - 6

Total - 72

##### Teaching language

Português

### Prerequisites

The student must be familiar with mathematics taught at pre-university level in Portugal (12nd level - science area).

### Bibliography

Bibliography:

1. Ferreira, J.C., *Elementos de Lógica Matemática e Teoria dos Conjuntos*, 2001

2. Johnson, D. L., *Elements of Logic via Numbers and Sets*, Springer Undergraduate Mathematics Series, 1998

3. Krantz, S. G., *The elements of advanced Mathematics*, CRC Press, 1995

4. Sebastião e Silva, J., *Compêndio de Matemàtica*, Curso Complementar do Ensino Secundário, 1º volume, 1º tomo, GAP-MEC 1995

5. Velleman, D. J., *How to prove it*, Cambridge University Press, 1994

### Teaching method

There are classes in which theory is lectured and illustrated by examples. There are also problem-solving sessions. For each chapter there is a list of proposed exercises that the students should solve. Most of the exercises is corrected in theproblem-solving sessions.

### Evaluation method

Students enrolled for the first time in the unit must attend all classes, except up to 3 lectures and up to 3 problem-solving classes.

Students that have already been enrolled in the unit must attend, at least, 2/3 of the lectures and 2/3 of the problem-solving classes.

The students that do not fulfill the above requirements automatically fail "Introdução à Lógica e Matemática Elementar".

There are two mid-term tests. These tests can substitute the final exam if the student has CT, at least, 9.5. CT is the arithmetic mean of the non-rounded grades of the tests.

If the student satisfies the conditions above with CT (rounded to units) greater than 16, he may choose between having 16 as final grade or undertake a complementary assessment.

To be approved in final exam, the student must have a minimum grade of 9.5 in it. Again, for grades (rounded to units) greater than 16, the student must undertake a complementary assessment, otherwise his final grade will be 16.

More detailed rules are available in the portuguese version.

The non-portuguese students should address the professor to ask any question that is not in this english version.

Eventual omitted subjects will be decided by the unit responsible.

## Subject matter

1. Sentential and quantificational logic.

2. Basic operations on sets.

3. Proof strategies.

4. Relations: equivalence and order relations.

5. Functions.

6. Mathematical induction and divisibility.

7. Finite and infinite sets.

8. Integers modulo n (optional).