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A word equation is a formal equality:= = between a pair of words and , each over an alphabet comprising both constants (c.f. ) and unknowns (c.f. ). [1] An assignment of constant words to the unknowns of is said to solve if it maps both sides of to identical words.
Venn diagram of (true part in red) In logic and mathematics, the logical biconditional, also known as material biconditional or equivalence or biimplication or bientailment, is the logical connective used to conjoin two statements and to form the statement "if and only if" (often abbreviated as "iff " [1]), where is known as the antecedent, and the consequent.
Corner quotes, also called “Quine quotes”; for quasi-quotation, i.e. quoting specific context of unspecified (“variable”) expressions; [4] also used for denoting Gödel number; [5] for example “āGā” denotes the Gödel number of G. (Typographical note: although the quotes appears as a “pair” in unicode (231C and 231D), they ...
The most thoroughly researched branch of propositional logic is classical truth-functional propositional logic, [1] in which formulas are interpreted as having precisely one of two possible truth values, the truth value of true or the truth value of false. [19]
If E and F are logical predicates, is true if E and F are both true. It is often replaced by the word "and" or the symbol "& ". 2. In lattice theory, denotes the meet or greatest lower bound operation. 3. In multilinear algebra, geometry, and multivariable calculus, denotes the wedge product or the exterior product. ā»
However, the converse of a statement with mutually inclusive terms remains true, given the truth of the original proposition. This is equivalent to saying that the converse of a definition is true. Thus, the statement "If I am a triangle, then I am a three-sided polygon" is logically equivalent to "If I am a three-sided polygon, then I am a ...
In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). [ 1 ] [ 2 ] Alternative names are switching function , used especially in older computer science literature, [ 3 ] [ 4 ] and truth function (or logical function) , used in logic .
Then , because any valuation satisfying will make true—and thus makes true. It follows from the definition that if a formula R {\displaystyle R} is a contradiction, then R {\displaystyle R} tautologically implies every formula, because there is no truth valuation that causes R {\displaystyle R} to be true, and so the definition of ...