For a given
implication a implies b, the converse is
b implies a. The converse is
logically equivalent to the
inverse, just as the implication is logically equivalent to its
contrapositive. An
example implication is "If I win the
lottery, then I will buy a boat," and its converse is "If I buy a
boat, then I have won the lottery." Below is a
truth table for an implication and its converse:
a | b | a --> b | b --> a
---------------------------
T | T | T | T
T | F | F | T
F | T | T | F
F | F | T | T
From the above, it should be clear that an implication and its converse are not usually equivalent; in fact, the only time they are equivalent is in the situation
a iff b (a if and only if b).