reverse vs converse vs inverse

First, it helps to look at the verb usage: you can reverse something, but you
cannot inverse or converse something.

The distinctions between reverse, converse, and inverse can often be made by looking at their roots and simple
forms.

Reverse - look at revert. It means to return to a former condition, position, etc. The root is from the Latin
reversus, which means to turn back. Reverse is often used to describe a directional change.

"I reversed my position on the matter."

"The water is now flowing in reverse."

Converse - look at convert. It means to change from one form to another. The root is from the Latin converses,
which means to turn around. Converse is often used to describe the 'exact' opposite.

"Black is the converse color of white."

"Jill is a democrat; conversely, Jack is a republican."

Inverse - look at invert. It means to turn upside down or inside out. The Latin root, inversus, means the
same. Inverse is often used to compare how two things are related in an opposite matter.

"The inverse of 1,2,3,4 is 4,3,2,1." *note that reverse is a process of inversion

"The relationship between the amounts of water in a container is inverse to the amount of space; the amount
of space decreases as the amount of water increases." *note that the reverse of this is not true

When used in logical or mathematical
statements:

If the statement is: if p then q

* converse:
if q then p

* inverse:
if not p then not q

* contrapositive:
if not q then not p

If a statement is true, the contrapositive is also logically true. Likewise, when the converse is true, the
inverse is also logically true.