What is logical equivalence? - Definition from WhatIs.com


logical equivalence

Part of the Computing fundamentals glossary:

Logical equivalence is a type of relationship between two statements or sentences in propositional logic or Boolean algebra. The relation translates verbally into "if and only if" and is symbolized by a double-lined, double arrow pointing to the left and right ( ). If A and B represent statements, then A B means "A if and only if B."

The statement A B is exactly the same as

(A B) * (B A)

where the asterisk (*) represents the logical AND operation, and the right-pointing, double-lined arrow ( ) represents logical implication.

Logical equivalence works both ways. Thus,

(A B) (B A)

Logical equivalence is important in the design of digital circuits. Several circuits may be logically equivalent, in that they all have identical truth table s. The goal of the engineer is to find the circuit that performs the desired logical function using the least possible number of gates. This will result in optimal operating efficiency, reliability, and speed.

Also see Mathematical Symbols .

This was last updated in September 2005
Posted by: Margaret Rouse

Related Terms


  • irrational number

    - An irrational number is a real number that cannot be reduced to any ratio between an integer p and a natural number q. (WhatIs.com)

  • Cartesian coordinates (rectangular coordinates)

    - Cartesian coordinates, also called rectangular coordinates, provide a method of rendering graphs and indicating the positions of points on a two-dimensional (2D) surface or in three-dimensional (3D... (WhatIs.com)

  • algorithm

    - An algorithm (pronounced AL-go-rith-um) is a procedure or formula for solving a problem. Algorithms are used throughout almost all areas of information technology. (WhatIs.com)


  • Computing fundamentals

    - Terms related to computer fundamentals, including computer hardware definitions and words and phrases about software, operating systems, peripherals and troubleshooting.

  • Internet applications

    - This WhatIs.com glossary contains terms related to Internet applications, including definitions about Software as a Service (SaaS) delivery models and words and phrases about web sites, e-commerce ...

Ask a Question About logical equivalencePowered by ITKnowledgeExchange.com

Get answers from your peers on your most technical challenges

Tech TalkComment



    Contribute to the conversation

    All fields are required. Comments will appear at the bottom of the article.