Search results
Results From The WOW.Com Content Network
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.
In logic, negation, also called the logical not or logical complement, is an operation that takes a proposition to another proposition "not ", written , , ′ [1] or ¯. [ citation needed ] It is interpreted intuitively as being true when P {\displaystyle P} is false, and false when P {\displaystyle P} is true.
In mathematics and mathematical logic, Boolean algebra is a branch of algebra.It differs from elementary algebra in two ways. First, the values of the variables are the truth values true and false, usually denoted 1 and 0, whereas in elementary algebra the values of the variables are numbers.
The NOT gate outputs a zero when given a one, and a one when given a zero. Hence, it inverts its inputs. Colloquially, this inversion of bits is called "flipping" bits. [1] As with all binary logic gates, other pairs of symbols — such as true and false, or high and low — may be used in lieu of one and zero.
In Boolean logic, logical NOR, [1] non-disjunction, or joint denial [1] is a truth-functional operator which produces a result that is the negation of logical or.That is, a sentence of the form (p NOR q) is true precisely when neither p nor q is true—i.e. when both p and q are false.
Though signatures might in some cases imply how non-logical symbols are to be interpreted, interpretation of the non-logical symbols in the signature is separate (and not necessarily fixed). Signatures concern syntax rather than semantics. In this approach, every non-logical symbol is of one of the following types:
A Boolean value is either true or false. A Boolean expression may be composed of a combination of the Boolean constants True/False or Yes/No, Boolean-typed variables, Boolean-valued operators, and Boolean-valued functions. [1] Boolean expressions correspond to propositional formulas in logic and are a special case of Boolean circuits. [2]
The corresponding logical symbols are "", "", [6] and , [10] and sometimes "iff".These are usually treated as equivalent. However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the first, ↔, is used as a symbol in logic formulas, while ⇔ is used in reasoning about those logic formulas ...