Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Logic and Truth Tables

In course

MATH-101(g): Analysis I

Étudier les concepts fondamentaux d'analyse et le calcul différentiel et intégral des fonctions réelles d'une variable. ...

Description

This lecture covers the concepts of logic, truth tables, and mathematical propositions. It explains how to interpret truth tables, define mathematical propositions, and analyze logical statements. The instructor demonstrates the process of constructing truth tables and understanding logical equivalences.

Instructors (2)

Annalisa Buffa

Lénaïc Chizat

Official source

Ontological neighbourhood

Logic

Classical logic: First-order logic

Related concepts (32)

Logical truth

Logical truth is one of the most fundamental concepts in logic. Broadly speaking, a logical truth is a statement which is true regardless of the truth or falsity of its constituent propositions. In other words, a logical truth is a statement which is not only true, but one which is true under all interpretations of its logical components (other than its logical constants). Thus, logical truths such as "if p, then p" can be considered tautologies.

Logical equivalence

In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. The logical equivalence of and is sometimes expressed as , , , or , depending on the notation being used. However, these symbols are also used for material equivalence, so proper interpretation would depend on the context. Logical equivalence is different from material equivalence, although the two concepts are intrinsically related. In logic, many common logical equivalences exist and are often listed as laws or properties.

Logic

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the science of deductively valid inferences or logical truths. It studies how conclusions follow from premises due to the structure of arguments alone, independent of their topic and content. Informal logic is associated with informal fallacies, critical thinking, and argumentation theory. It examines arguments expressed in natural language while formal logic uses formal language.

Philosophy of mathematics

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics. It aims to understand the nature and methods of mathematics, and find out the place of mathematics in people's lives. The logical and structural nature of mathematics makes this branch of philosophy broad and unique. The philosophy of mathematics has two major themes: mathematical realism and mathematical anti-realism. The origin of mathematics is of arguments and disagreements.

Truth table

A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. In particular, truth tables can be used to show whether a propositional expression is true for all legitimate input values, that is, logically valid.

Related lectures (32)

Concept of Proof in Mathematics

Delves into the concept of proof in mathematics, emphasizing the importance of evidence and logical reasoning.

Propositional Logic: Basics and Applications

Covers the basics of propositional logic, its history, language, and computing applications.

Introduction & Propositional Logic

Covers the basics of propositional logic, logical connectives, truth tables, and compound propositions.

Propositional Logic: Translations and Equivalences

Covers translating natural language to propositional logic and proving tautologies.

Propositional Logic: Implication and Compound Propositions

Covers logical connectives, implication, biconditional, and compound propositions in propositional logic.

Related concepts (32)

Logical truth

Logical equivalence

Logic

Philosophy of mathematics

Truth table