# converse

### Graph Theory

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

### Logic

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.)

### Sneakers

The Converse™ sneaker is a classic design and very comfortable, with an all-canvas upper and rubber sole. Figure 1: Converse™ sneaker (high-top). 