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- https://math.libretexts.org/Bookshelves/Combinatorics_and_Discrete_Mathematics/A_Spiral_Workbook_for_Discrete_Mathematics_(Kwong)/02%3A_Logic/2.01%3A_PropositionsThe rules of logic allow us to distinguish between valid and invalid arguments. Besides mathematics, logic has numerous applications in computer science, including the design of computer circuits and ...The rules of logic allow us to distinguish between valid and invalid arguments. Besides mathematics, logic has numerous applications in computer science, including the design of computer circuits and the construction of computer programs. To analyze whether a certain argument is valid, we first extract its syntax.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_220_Discrete_Math/2%3A_Logic/2.1%3A_PropositionsThe claim is true if A is a real number, but it is not always true if A is a matrix 1 . Thus, it is not a proposition. The result is called the negation of p, and is denoted ∼p or ...The claim is true if A is a real number, but it is not always true if A is a matrix 1 . Thus, it is not a proposition. The result is called the negation of p, and is denoted ∼p or ¬p, both of which are pronounced as “not p.” The similarity between the notations ∼p and −x is obvious. We can also write the negation of p as ¯p, which is pronounced as “p bar.” The truth value of ¯p is opposite of that of p.
- https://math.libretexts.org/Courses/Stanford_Online_High_School/Logic_for_All%3A_An_Introduction_to_Logical_Reasoning/03%3A_Propositional_LogicThis page discusses propositional logic, emphasizing its importance in structuring reasoning through propositions with defined truth values. It covers logical connectives, including negation, conjunct...This page discusses propositional logic, emphasizing its importance in structuring reasoning through propositions with defined truth values. It covers logical connectives, including negation, conjunction, and disjunction, and introduces the exclusive or (XOR), discussing the role of parentheses and precedence. The text highlights practical applications in fields like computer science and law, addresses common misconceptions, and provides exercises for better understanding.
- 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.
