Converse (logic)

In mathematics and logic, a converse is a variant of an implication. More specifically, given an implication of the form formula_1, the converse is the statement formula_2. 
While a converse is similar to its originating implication, they are not logically equivalent. This means that the truth of an implication does not guarantee the truth of its converse (and vice versa).
As a logical connective, the converse of formula_3 and formula_4 can be represented by the symbol formula_5 (as in formula_6).