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).