To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Logical equality

From Wikipedia, the free encyclopedia

Logical equality
EQ, XNOR
Venn diagram of Logical equality
Definition
Truth table
Logic gate
XNOR ANSI.svg
Normal forms
Disjunctive
Conjunctive
Zhegalkin polynomial
Post's lattices
0-preservingno
1-preservingyes
Monotoneno
Affineyes

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.

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 left 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 right 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" or "⊕". 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:

This explains why "EQ" is often called "XNOR" in the combinational logic of circuit engineers, since it is the negation of the XOR operation; "NXOR" is a less commonly used alternative.[1] 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".

Definition

Logical equality is an operation on two logical values, typically the values of two propositions, that produces a value of true if and only if both operands are false or both operands are true.

The truth table of p EQ q (also written as p = q, p ↔ q, Epq, p ≡ q, or p == q) is as follows:

The Venn diagram of A EQ B (red part is true)
The Venn diagram of A EQ B (red part is true)
Logical equality
p q p = q
0 0 1
0 1 0
1 0 0
1 1 1

Alternative descriptions

The form (x = y) is equivalent to the form (xy) ∨ (¬x ∧ ¬y).

For the operands x and y, the truth table of the logical equality operator is as follows:

y
T F
x T T F
F F T

See also

References

  1. ^ Keeton, Brian; Cavaness, Chuck; Friesen, Geoff (2001), Using Java 2, Que Publishing, p. 112, ISBN 9780789724687.

External links

This page was last edited on 9 February 2021, at 18:09
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.