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A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, Boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables. [1]
It is equivalent to the logical connective from mathematical logic, also known as the material biconditional. The two-input version implements logical equality, behaving according to the truth table to the right, and hence the gate is sometimes called an "equivalence gate". A high output (1) results if both of the inputs to the gate are the same.
Under this convention, the law of identity is a logical truth. In first-order logic without identity , identity is treated as an interpretable predicate and its axioms are supplied by the theory. This allows a broader equivalence relation to be used that may allow a = b to be satisfied by distinct individuals a and b .
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
The NOR gate is a digital logic gate that implements logical NOR - it behaves according to the truth table to the right. A HIGH output (1) results if both the inputs to the gate are LOW (0); if one or both input is HIGH (1), a LOW output (0) results. NOR is the result of the negation of the OR operator.
Due to the ability to speak about non-logical individuals along with the original logical connectives, first-order logic includes propositional logic. [ 7 ] : 29–30 The truth of a formula such as " x is a philosopher" depends on which object is denoted by x and on the interpretation of the predicate "is a philosopher".
In logic and mathematics, statements and are said to be logically equivalent if they have the same truth value in every model. [1] The logical equivalence of p {\displaystyle p} and q {\displaystyle q} is sometimes expressed as p ≡ q {\displaystyle p\equiv q} , p :: q {\displaystyle p::q} , E p q {\displaystyle {\textsf {E}}pq} , or p q ...
The logic of here and there (HT, also referred as Smetanov logic SmT or as Gödel G3 logic), introduced by Heyting in 1930 [21] as a model for studying intuitionistic logic, is a three-valued intermediate logic where the third truth value NF (not false) has the semantics of a proposition that can be intuitionistically proven to not be false ...