Graph Theory

The converse of a directed graph is obtained by reversing the direction of each edge.


A converse statement is a statement derived from a conditional by swapping the antecedent and consequent. Thus the converse of the conditional statement ‘if \(A\) then \(B\)’ is ‘if \(B\) then \(A\).’ In symbolic logic this is written as \(B \rightarrow A\).

A conditional and its converse are not logically equivalent, but the converse and the inverse are equivalent, being contrapositives of each other.

Set Theory

The converse of any binary relation is obtained by reversing the order of the pairs making up the relation. That is, if \(R\) is a relation, then \((b,a)\) is in the converse of \(R\) if and only if \((a,b)\) is in \(R\). (Somewhat confusingly, we speak of the inverse of a one-to-one function to mean the same thing.)


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Figure 1: Converse™ sneaker (high-top).