Search results
Results From The WOW.Com Content Network
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.
The biconditional is true in two cases, where either both statements are true or both are false. The connective is biconditional (a statement of material equivalence), [2] and can be likened to the standard material conditional ("only if", equal to "if ... then") combined with its reverse ("if"); hence the name. The result is that the truth of ...
material biconditional (material equivalence) if and only if, iff, xnor propositional logic, Boolean algebra: is true only if both A and B are false, or both A and B are true. Whether a symbol means a material biconditional or a logical equivalence, depends on the author’s style.
Logical equivalence is different from material equivalence. Formulas and are logically equivalent if and only if the statement of their material equivalence is a tautology.
A system of symbols and rules for manipulating these symbols, used to derive statements or theorems in a logical or mathematical domain. formation rules Rules that specify the correct ways in which the basic symbols of a formal language can be combined to form well-formed formulas. formula
Equivalence is symbolized with ⇔ and is a metalanguage symbol, while a biconditional is symbolized with ↔ and is a logical connective in the object language . Regardless, an equivalence or biconditional is true if, and only if, the formulas connected by it are assigned the same semantic value under every interpretation.
Biconditional elimination is the name of two valid rules of inference of propositional logic. It allows for one to infer a conditional from a biconditional . If P ↔ Q {\displaystyle P\leftrightarrow Q} is true, then one may infer that P → Q {\displaystyle P\to Q} is true, and also that Q → P {\displaystyle Q\to P} is true. [ 1 ]
A mathematical symbol is a figure or a combination of figures that is used to represent a mathematical object, an action on mathematical objects, a relation between mathematical objects, or for structuring the other symbols that occur in a formula. As formulas are entirely constituted with symbols of various types, many symbols are needed for ...