# Converse implication

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

It may take the following forms:

p⊂q, Bpq, or p←q

## Definition

### Truth table

The truth table of A⊂B

a b
T T T
T F T
F T F
F F T

### Venn diagram

The Venn diagram of "If B then A" (the white area shows where the statement is false)

## 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.

## Natural language

"Not q without p."

"p if q."

(A + B')