In logic Logic, from the Greek λογικός is the study of reasoning. Logic is used in most intellectual activity, but is studied primarily in the disciplines of philosophy, mathematics, and computer science. Logic examines general forms which arguments may take, which forms are valid, and which are fallacies. It is one kind of critical thinking. In, a logical connective (also called a logical operator) is a symbol A symbol is an idea, abstraction or concept, tokens of which may be marks or a configuration of marks which form a particular pattern. Although the term "symbol" in common use refers at some times to the idea being symbolized, and at other times to the marks on a piece of paper or chalkboard which are being used to express that idea; in or word A word is the smallest free form in a language, in contrast to a morpheme, which is the smallest unit of meaning. A word may consist of only one morpheme (e.g. wolf), but a single morpheme may not be able to exist as a free form (e.g. the English plural morpheme -s) used to connect two or more sentences In the field of linguistics, a sentence —an expression in natural language— is often defined to indicate a grammatical and lexical unit consisting of one or more words that represent distinct concepts. A sentence can include words grouped meaningfully to express a statement, question, exclamation, request or command (of either a formal A formal language is a set of words, i.e. finite strings of letters, symbols, or tokens. The set from which these letters are taken is called the alphabet over which the language is defined. A formal language is often defined by means of a formal grammar ; accordingly, words that belong to a formal language are sometimes called well-formed words ( or a natural In the philosophy of language, a natural language is any language which arises in an unpremeditated fashion as the result of the innate facility for language possessed by the human intellect. A natural language is typically used for communication, and may be spoken, signed, or written. Natural language is distinguished from constructed languages language) in a grammatically valid In logic, syntax is anything having to do with formal languages or formal systems without regard to any interpretation or meaning given to them. Syntax is concerned with the rules used for constructing, or transforming the symbols and words of a language, as contrasted with the semantics of a language which is concerned with its meaning way, such that the compound sentence produced has a truth value In logic and mathematics, a logical value, also called a truth value, is a value indicating the relation of a proposition to truth dependant on the respective truth values of the original sentences.
Each logical connective can be expressed as a function In mathematics, a function is a relation between a given set of elements and another set of elements (the codomain), which associates each element in the domain with exactly one element in the codomain. The elements so related can be any kind of thing (words, objects, qualities) but are typically mathematical quantities, such as real numbers, called a truth function In mathematical logic, a truth function is a function from a set of truth-values to truth-values. Classically the domain and range of a truth function are {truth,falsehood}, but generally they may have any number of truth-values, including an infinity of them. A sentential connective is called "truth functional" if it is assigned or. For this reason, logical connectives are sometimes called truth-functional connectives. The most common logical connectives are binary connectives (also called dyadic connectives) which join two sentences whose truth values can be thought of as the function's operands An operand is a quantity on which an operation is performed. The following arithmetic expression shows an example of operators and operands:. Also commonly, negation In logic and mathematics, negation is an operation on propositions. For example, in classical logic negation is normally interpreted by the truth function that takes truth to falsity and vice versa. In intuitionistic logic, according to the Brouwer-Heyting-Kolmogorov interpretation, the negation of a proposition P is the proposition whose proofs is considered to be a unary connective.
Logical connectives along with quantifiers Quantification has two distinct sense. In mathematics and empirical science, it is the act of counting and measuring that maps human sense observations and experiences into members of some set of numbers. Quantification in this sense is fundamental to the scientific method are the two main types of logical constants In mathematical logic, a logical constant of a language is a symbol that has the same semantic value under every interpretation of . Two important types of logical constants are logical connectives and quantifiers. The equality predicate is also treated as a logical constant in many systems of logic used in formal systems In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive (to conclude) one expression from one or more other expressions (premises) antecedently supposed (axioms) or derived (theorems). The axioms and rules may be called a deductive apparatus. A formal system may be formulated and studied for its such as propositional logic In mathematical logic, a propositional calculus or logic is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules and axioms allows certain formulas to be derived, called theorems; which may be interpreted as true propositions. The series of formulas which is constructed and predicate logic In mathematical logic, predicate logic is the generic term for symbolic formal systems like first-order logic, second-order logic, many-sorted logic or infinitary logic. This formal system is distinguished from other systems in that its formulas contain variables which can be quantified. Two common quantifiers are the existential ∃ and universal.
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By logical consequence it follows then that building more muscle will better enhance the fat burning process. The key with any form of resistance ...
Q. Given 1. Logic if difficult or not many students like logic 2. If mathematics is easy, then logic is not difficult By translating these assumptions into statements involving propositional variables and logical connectives, determine if this is a valid conclusion: That if not many students like logic, then either mathematics is not easy or logic is not difficult. A similar one was: That logic is not difficult or mathematics is not easy. Let p = logic is difficult q = many students like logic r = math is easy P or q given A similar one was: That logic is not difficult or mathematics is not easy. Let p = logic is difficult q = many students like logic r = math is easy P or q given r implies not p given not r or not p not p or not r… [cont.]
Asked by CH - Fri Apr 13 10:23:31 2007 - - 2 Answers - 0 Comments
A. Thanks for the update. Might have been good information before I made that ridiculous post.
Answered by dietdewdude887 - Fri Apr 13 10:28:33 2007
