# 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.