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- https://math.libretexts.org/Courses/Stanford_Online_High_School/Logic_for_All%3A_An_Introduction_to_Logical_Reasoning/04%3A_Truth_TablesThis page highlights the importance of truth tables in logic, demonstrating their role in evaluating compound statements and logical connectives. It emphasizes their applications in diverse fields lik...This page highlights the importance of truth tables in logic, demonstrating their role in evaluating compound statements and logical connectives. It emphasizes their applications in diverse fields like argument validation, circuit design, and software testing. Additionally, the page addresses the use of truth tables in analyzing access control conditions for user authentication, clarifying misconceptions around logical operators.
- https://math.libretexts.org/Courses/Stanford_Online_High_School/Logic_for_All%3A_An_Introduction_to_Logical_Reasoning/06%3A_The_Converse_and_the_ContrapositiveThis page covers the concepts of converses and contrapositives in logic, explaining their significance and truth values. It highlights that the converse may not be true while the contrapositive is log...This page covers the concepts of converses and contrapositives in logic, explaining their significance and truth values. It highlights that the converse may not be true while the contrapositive is logically equivalent to the original statement. Examples clarify common misconceptions, and exercises are provided for practice. It discusses logical implications, specifically p→q, its converse, and contrapositive while addressing logical errors.
- https://math.libretexts.org/Courses/Stanford_Online_High_School/Logic_for_All%3A_An_Introduction_to_Logical_Reasoning/08%3A_Representing_Statements_SymbolicallyThis page emphasizes the significance of symbolic representation in logic through a house-and-blueprint analogy, detailing five propositional connectives and the necessity of parentheses to prevent am...This page emphasizes the significance of symbolic representation in logic through a house-and-blueprint analogy, detailing five propositional connectives and the necessity of parentheses to prevent ambiguity. It includes exercises for practicing logical translation and concepts like implications, conjunctions, and disjunctions while maintaining meaning in restructured statements.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/02%3A_Logic/2.01%3A_Formal_LogicThis page defines statements and distinguishes them from non-statements, introduces logic operations and truth tables for combining statements, and explains equivalence of statements using DeMorgan's ...This page defines statements and distinguishes them from non-statements, introduces logic operations and truth tables for combining statements, and explains equivalence of statements using DeMorgan's Laws. It highlights conditions for compound statements to be false and includes practice checklists for truth tables and equivalence inquiries from previous exercises.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/01%3A_Basics/1.01%3A_TerminologyThis page discusses the structure of mathematics, emphasizing the importance of proofs and fundamental categories like undefined terms, defined terms, axioms, and theorems. Undefined terms prevent inf...This page discusses the structure of mathematics, emphasizing the importance of proofs and fundamental categories like undefined terms, defined terms, axioms, and theorems. Undefined terms prevent infinite definitions, while defined terms rely on these and established definitions. Axioms are unproven statements serving as a foundation for deriving new statements. Mastering these concepts is essential for solving mathematical problems.
- https://math.libretexts.org/Courses/Stanford_Online_High_School/Logic_for_All%3A_An_Introduction_to_Logical_Reasoning/12%3A_Logic_Learning_ResourcesThis page provides a curated list of resources for learning logic, suitable for beginners and advanced learners. It includes recommended university courses from institutions like Stanford and MIT, onl...This page provides a curated list of resources for learning logic, suitable for beginners and advanced learners. It includes recommended university courses from institutions like Stanford and MIT, online tutorials, books, and platforms like Khan Academy for interactive learning. Users are encouraged to engage with online communities for support. Logic4All remains neutral and does not endorse specific resources.
- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/Discrete_Mathematics_for_Computer_Science_(Fitch)/03%3A_Functions/3.02%3A_Boolean_AlgebraThis page explores the connection between arithmetic operations and Boolean algebra, detailing terminology and definitions relevant to Boolean functions. It highlights methods for representing and sim...This page explores the connection between arithmetic operations and Boolean algebra, detailing terminology and definitions relevant to Boolean functions. It highlights methods for representing and simplifying these functions through algebraic techniques. The text includes practical exercises for evaluating and designing Boolean functions and their circuit representations, aiming to demonstrate the optimization of logical expressions for various applications.
- https://math.libretexts.org/Courses/Stanford_Online_High_School/Logic_for_All%3A_An_Introduction_to_Logical_Reasoning/10%3A_Predicate_LogicThis page discusses the enhancements of predicate logic over propositional logic, focusing on object properties and relationships using quantifiers. It explains translation of English statements into ...This page discusses the enhancements of predicate logic over propositional logic, focusing on object properties and relationships using quantifiers. It explains translation of English statements into predicate logic, clarifies common misconceptions about quantifiers, and emphasizes practical applications in fields like AI and mathematics. The text also includes exercises to practice translating statements, underscoring the importance of precision in logical understanding.
- https://math.libretexts.org/Courses/Stanford_Online_High_School/Logic_for_All%3A_An_Introduction_to_Logical_Reasoning/05%3A_If-Then_StatementsThis page highlights the significance of if-then statements in programming, logic, and decision-making across disciplines like law and medicine. It explains how mastering these logical constructs prev...This page highlights the significance of if-then statements in programming, logic, and decision-making across disciplines like law and medicine. It explains how mastering these logical constructs prevents errors and enhances reasoning. Exercises on rewriting statements, identifying hypotheses and conclusions, and applying Modus Ponens and Modus Tollens are included for reinforcement.