A CONDITIONAL statement is one of the form P –> Q.  (P implies Q; if P, then Q; etc.) 

EXAMPLE:  If you have 4 quarters, then you have change for a dollar.

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The CONVERSE of a conditional statement is Q –> P.  (It’s where the phrase ‘and conversely’ comes from in daily English usage.)

EXAMPLE: If you have change for a dollar, then you have 4 quarters.  

Note that while that may be true, it doesn’t necessarily follow.  Concluding that is does follow is to be guilty of The Fallacy of the Converse.

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The INVERSE of a conditional statement is [Not P] –> [Not Q].

EXAMPLE: If you don’t have 4 quarters, then you don’t have change for a dollar. 

Note that while that may be true, it doesn’t necessarily follow.  Concluding that does follow is to be guilty of The Fallacy of the Inverse.

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The CONTRAPOSITIVE of a conditional statement is [Not Q] –> [Not P].

EXAMPLE: If you don’t have change for a dollar, then you don’t have 4 quarters. 

Note that this DOES necessarily follow!!  We say that the Conditional and the Contrapositive are logically equivalent.

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Side note (ignore if you wish).  We also note that the Converse and Inverse are logically equivalent to each other.  (Since one is the Contrapositive of the other.)