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Implication

Category
STANDARD MATHEMATICS
Definition
A logical relation in which one statement being true guarantees another statement.
Math Level
GENERAL

An implication is a logical statement of the form “if A, then B”, often written A⇒BA\Rightarrow B.

It is directional: knowing that A implies B does not automatically mean that B implies A. This is why sufficient, necessary and equivalent conditions must be distinguished carefully.

See also: sufficient condition, necessary condition, equivalent condition, conditional theorem..

Related glossary terms

  1. [..]Conditional theoremGLOSSARY · STANDARD MATHEMATICS
  2. [..]Equivalent conditionGLOSSARY · STANDARD MATHEMATICS
  3. [..]Necessary conditionGLOSSARY · STANDARD MATHEMATICS
  4. [..]Sufficient conditionGLOSSARY · STANDARD MATHEMATICS

Read this term in context

  1. [..]Conditional theoremARTICLE · ART-RC-0034
  2. [..]Equivalent conditionARTICLE · ART-RC-0041
  3. [..]Necessary conditionARTICLE · ART-RC-0040
  4. [..]Sufficient conditionARTICLE · ART-RC-0039