Let a statement be of the form of an implication

If then

i.e. it has a certain premise and a conclusion . The statement in which one has interchanged the conclusion and the premise,

If then

is the converse of the first. In other words, from the former one concludes that is necessary for , and from the latter that is necessary for .

Note that the converse of an implication and the inverse of the same implication are contrapositives of each other and thus are logically equivalent.

If the original statement is a theorem that is known to be true, then its converse is the converse theorem of the original statement. Note that, if the converse theorem of a true theorem “If then ” is also true, then “ iff ” is a true theorem.

For example, we know the theorem on isosceles triangles:

If a triangle contains two congruent sides, then it has two congruent angles.

There is also its converse theorem:

If a triangle contains two congruent angles, then it has two congruent sides.

Both of these theorems are true (see the entries angles of an isosceles triangle and determining from angles that a triangle is isosceles, respectively). But there are many true theorems whose converse theorem is not true, e.g.:

If a function is differentiable on an interval , then it is continuous on .