You're given an if-then statement which has the structure
"If A, then B"
where A and B are some events.
The converse of this kind of statement reverses the roles of A and B, so that it would say
"If B, then A"
Not to be confused with the inverse, which is the negation of both events and says
"If <em>not</em> A, then <em>not</em> B"
as well as the contrapositive, which is the converse of the inverse, and says
"If <em>not</em> B, then <em>not</em> A"
A bi-conditional statement is sort of a combination of the original statement and the converse, one that says both
"If A, then B"
as well as
"If B, then A"
which means that given either A or B, the other one is also true. Typically this gets condensed into one statement in the form
"A if and only if B"
(and sometimes "if and only if" is abbreviated "iff")
For the given statement,
"If a person is the 44th President of the United States, then that person is Barack Obama"
the converse would be
"If a person is Barack Obama, then that person is the 44th President of the United States"
Then a bi-conditional version of this statement would be
"A person is the 44th President of the United States <em>if and only if</em> that person is Barack Obama"
