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- https://math.libretexts.org/Courses/Fullerton_College/Math_100%3A_Liberal_Arts_Math_(Claassen_and_Ikeda)/05%3A_Logic/5.01%3A_Logic_StatementsLogic is the study of the methods and principles of reasoning. In logic, statement is a declarative sentence that is either true or false, but not both. The key to constructing a good logical statemen...Logic is the study of the methods and principles of reasoning. In logic, statement is a declarative sentence that is either true or false, but not both. The key to constructing a good logical statement is that there must be no ambiguity. To be a statement, a sentence must be true or false. It cannot be both. In logic, the truth of a statement is established beyond ANY doubt by a well-reasoned argument.
- https://math.libretexts.org/Courses/Rio_Hondo/Math_150%3A_Survey_of_Mathematics/03%3A_Logic/3.02%3A_Logic/3.2.03%3A_Quantified_StatementsIn contrast, words or phrases such as “some”, “one”, or “at least one” are called existential quantifiers because they describe the existence of at least one element in a set. The negation of “all A a...In contrast, words or phrases such as “some”, “one”, or “at least one” are called existential quantifiers because they describe the existence of at least one element in a set. The negation of “all A are B” is “at least one A is not B”. The negation of “no A are B” is “at least one A is B”. The negation of “at least one A is B” is “no A are B”. The negation of “at least one A is not B” is “all A are B”.
- https://math.libretexts.org/Courses/American_River_College/Math_300%3A_My_Math_Ideas_Textbook_(Kinoshita)/05%3A_Logic/5.01%3A_Logic/5.1.04%3A_Quantified_StatementsIn contrast, words or phrases such as “some”, “one”, or “at least one” are called existential quantifiers because they describe the existence of at least one element in a set. Suppose your friend says...In contrast, words or phrases such as “some”, “one”, or “at least one” are called existential quantifiers because they describe the existence of at least one element in a set. Suppose your friend says “One of these six cartons of milk is leaking.” What is the minimum amount of evidence you would need to prove your friend wrong? The negation of “all A are B” is “at least one A is not B”. The negation of “at least one A is not B” is “all A are B”.
- https://math.libretexts.org/Courses/Chabot_College/Math_in_Society_(Zhang)/06%3A_Logic/6.01%3A_Statements_Connectives_and_QuantifiersA connective on a statement is a word or combination of words that combines one or more statements to make a new mathematical statement. A conditional statement is of the form "If ... then ..." and us...A connective on a statement is a word or combination of words that combines one or more statements to make a new mathematical statement. A conditional statement is of the form "If ... then ..." and uses the symbol \(\rightarrow\): If \(p\), then \(q\) is notated \(p \rightarrow q\) You can remember the first two symbols by relating them to the shapes for the union and intersection. \(A \wedge B\) would be the elements that exist in both sets, in \(A \cap B\).
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_300%3A_Mathematical_Ideas_Textbook_(Muranaka)/06%3A_Miscellaneous_Extra_Topics/6.02%3A_Logic/6.2.03%3A_Quantified_StatementsIn contrast, words or phrases such as “some”, “one”, or “at least one” are called existential quantifiers because they describe the existence of at least one element in a set. Suppose your friend says...In contrast, words or phrases such as “some”, “one”, or “at least one” are called existential quantifiers because they describe the existence of at least one element in a set. Suppose your friend says “One of these six cartons of milk is leaking.” What is the minimum amount of evidence you would need to prove your friend wrong? The negation of “all A are B” is “at least one A is not B”. The negation of “at least one A is not B” is “all A are B”.
- https://math.libretexts.org/Courses/Las_Positas_College/Math_for_Liberal_Arts/03%3A_Logic/3.01%3A_Statements_Connectives_and_QuantifiersA connective on a statement is a word or combination of words that combines one or more statements to make a new mathematical statement. A conditional statement is of the form "If ... then ..." and us...A connective on a statement is a word or combination of words that combines one or more statements to make a new mathematical statement. A conditional statement is of the form "If ... then ..." and uses the symbol \(\rightarrow\): If \(p\), then \(q\) is notated \(p \rightarrow q\) You can remember the first two symbols by relating them to the shapes for the union and intersection. \(A \wedge B\) would be the elements that exist in both sets, in \(A \cap B\).
