Converse implication

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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).

Definition

Truth table

The truth table of

T T T
T F T
F T F
F F T

Logical Equivalences

Converse implication is logically equivalent to the disjunction of and

    
Venn1101.svg      Venn0101.svg Venn1100.svg

Properties

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.

Symbol

←, ⇐ 

Natural language

"Not q without p."

"p if q."

See also