## NEKG33 Mathematical methods for economists

## Chapter 11 : Day 11: Logic and sets

### By Lund University

First day of the second part of the course. A fresh start is always nice. We do a complete reboot and start from the begining.

## Logic: Lectures

In this section, we explore very fundamental questions such as what exactly do we mean by a statement "x = 4". We will formally define fundamental terms such as predicates, implications and compound statement. We will also investigate various methods of constructing proofs in mathematics.

#### Statements and predicates

#### Mathematical implication

#### Compound statements and truth tables

#### Proofs

## Logic: Problems

Exercises on logic

#### Problem: Necessary and sufficient conditions

#### Problem: Implications and converse

#### Problem: if, only if, and if and only if

#### Problem: Implication and equivalence with squares

#### Problem: Proof that squares are non-negative

#### Problem: Proof with squares and inequalities

#### Problem: Proof with square and zero

#### Problem: Proof with sum of squares

#### Problem: Proof, cubes can be negative

#### Problem: Proof, fourth powers cannot be negative

#### Problem: Proof with squares and strict inequalities

#### Problem: Proof that cubic function is injective

## Sets: Lectures

This section is an introduction to an important topic in mathematics, namely set theory. Set theory is generally considered as a subtopic of mathematical logic. Informally, sets are collection of objects. We will introduce the basic notation, such as set membership and subsets. We will also look at some set algebra; union, intersection and complement. Finally, we look at Venn the diagram as a way of illustrating rules for set operations.

#### Sets

## Sets: Problems

Exercises on sets