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Logical equality is a logical operator that corresponds to equality in boolean algebra and to the logical biconditional in propositional calculus. It gives the functional value true if both functional arguments have the same logical value, and false if they are different. Image File history File links XNOR.JPG XNOR Logic Gate File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
Image File history File links XNOR.JPG XNOR Logic Gate File history Legend: (cur) = this is the current file, (del) = delete this old version, (rev) = revert to this old version. ...
In logical calculus, logical operators or logical connectors serve to connect statements into more complicated compound statements. ...
In mathematics, two mathematical objects are considered equal if they are precisely the same in every way. ...
Wikibooks has more about Boolean logic, under the somewhat misleading title Boolean Algebra For a basic intro to sets, Boolean operations, Venn diagrams, truth tables, and Boolean applications, see Boolean logic. ...
In logical calculus of mathematics, logical biconditional is a logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). ...
In mathematical logic the propositional calculus or sentential calculus is a formal deduction system whose atomic formulas are propositional variables. ...
Partial plot of a function f. ...
When someone sincerely agrees with an assertion, they might claim that it is the truth. ...
In logic and mathematics, a logical value, also called a truth value, is a value indicating to what extent a proposition is true. ...
FALSE is an esoteric programming language designed by Wouter van Oortmerssen in 1993, named after his favourite boolean value. ...
It is customary practice in various applications, if not always technically precise, to indicate the operation of logical equality on the logical operands x and y by any of the following forms:
 Some logicians, however, draw a firm distinction between a functional form, like those in the lefthand column, which they interpret as an application of a function to a pair of arguments — and thus a mere indication that the value of the compound expression depends on the values of the component expressions — and an equational form, like those in the righthand column, which they interpret as an assertion that the arguments have equal values, in other words, that the functional value of the compound expression is true.
In mathematics, the plus sign "+" almost invariably indicates an operation that satisfies the axioms assigned to addition in the type of algebraic structure that is known as a field. For boolean algebra, this means that the logical operation signified by "+" is not the same as the inclusive disjunction signified by "∨" but is actually equivalent to the logical inequality operator signified by "≠", or what amounts to the same thing, the exclusive disjunction signified by "XOR". Naturally, these variations in usage have caused some failures to communicate between mathematicians and switching engineers over the years. At any rate, one has the following array of corresponding forms for the symbols associated with logical inequality: Euclid, detail from The School of Athens by Raphael. ...
In universal algebra, a branch of pure mathematics, an algebraic structure consists of one or more sets closed under one or more operations. ...
This article presents the essential definitions. ...
Exclusive disjunction (usual symbol XOR occasionally EOR) is a logical operator that results in true if one of the operands, but not both of them, is true. ...
 This explains why "EQ" is often called "XNOR" in the combinational logic of circuit engineers, since it is the Negation of the XOR operation. Another rationalization of the admittedly circuitous name "XNOR" is that one begins with the "both false" operator NOR and then adds the eXception, "or both true". This article is not about combinatory logic, a topic in mathematical logic. ...
Exclusive disjunction (usual symbol xor) is a logical operator that results in true if one of the operands (not both) is true. ...
Alternative descriptions
The form (x = y) is equivalent to the form (x ∧ y) ∨ (¬x ∧ ¬y).
For the operands x and y, the truth table of the logical equality operator is as follows: Truth tables are a type of mathematical table used in logic to determine whether an expression is true or whether an argument is valid. ...
 | y | | T | F | | x | T | T | F | | F | F | T |
See also
Other operators Exclusive disjunction (usual symbol XOR occasionally EOR) is a logical operator that results in true if one of the operands, but not both of them, is true. ...
AND Logic Gate In mathematics, logical conjunction (usual symbol and) is a logical operator that results in false if either of the operands is false. ...
OR logic gate. ...
In propositional calculus, or logical calculus in mathematics, the material conditional or the implies operator is a binary truth-functional logical operator yielding the form If a then c, where a and c are statement variables (to be replaced by any meaningful indicative sentence of the language). ...
NAND Logic Gate The Sheffer stroke, |, is the negation of the conjunction operator. ...
NOR Logic Gate Logical nor (not or), joint denial, or Webb-operation is a boolean logic operator which produces a result that is the inverse of logical or. ...
Related topics Ampheck, from Greek double-edged, is a term coined by Charles Sanders Peirce for either one of the pair of logically dual operators, variously referred to as Peirce arrows, Sheffer strokes, or NAND and NNOR. Either of these logical operators is a sole sufficient operator for deriving or generating all...
Wikibooks has more about Boolean logic, under the somewhat misleading title Boolean Algebra For a basic intro to sets, Boolean operations, Venn diagrams, truth tables, and Boolean applications, see Boolean logic. ...
In mathematics, a boolean function is usually a function F(b1, b2, ..., bn) of a number n of boolean variables bi from the two-element boolean algebra B = {0, 1}, such that F also takes values in B. A function on an arbitrary set X taking values in B is...
Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the empty set, that is, a class of non-existent entities, such as round squares, without resorting to uncertain truth values. ...
In mathematical logic, propositional logic is the logic of mathematical objects called propositions. ...
Zeroth-order logic is a term in popular use among practitioners for the subject matter otherwise known as boolean functions, monadic predicate logic, propositional calculus, or sentential calculus. ...
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