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.
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.
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.
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.
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.)
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