Open main menu
Venn diagram of
(the white area shows where the statement is false)

Converse implication is the converse of implication, written ←. That is to say; that for any two propositions and , if implies , then is the converse implication of .

It is written , but may also be notated , or "Bpq" (in Bocheński notation).

Contents

DefinitionEdit

Truth tableEdit

The truth table of  

     
T T T
T F T
F T F
F F T

Logical EquivalencesEdit

Converse implication is logically equivalent to the disjunction of   and  

             
             

PropertiesEdit

truth-preserving: The interpretation under which all variables are assigned a truth value of 'true' produces a truth value of 'true' as a result of converse implication.

SymbolEdit

←, ⇐ 

Natural languageEdit

"Not q without p."

"p if q."

See alsoEdit