The
contrapositive
of a conditional statement is formed by negating both
the hypothesis and the conclusion, and then interchanging
the resulting negations.
In other words, the contrapositive negates and switches the parts of the sentence. It
does BOTH the jobs of the INVERSE and the CONVERSE.

Example:
Conditional: "If 9 is an odd number,
then 9 is divisible by 2."
(true)
(false) 
This statement is logically
FALSE. 



Contrapositive:
"If 9 is not
divisible by 2, then
9 is not an odd number."
(true)
(false) 
This statement is logically
FALSE. 


HINT:
Remember
that the contrapositive (a big long word) is really the
combining together of the strategies of two other
words: converse and inverse.



An
important fact to remember about the contrapositive, is that it always has the SAME truth value as the original conditional
statement. 
**If
the original statement is TRUE, the contrapositive is TRUE.
If the
original statement is FALSE, the contrapositive is FALSE.
They are said to
be logically
equivalent.
("equivalent"
means "the same")
A
truth table can be used to show that a conditional statement and
its contrapositive are logically equivalent.
Notice that the truth values
are the same.


Remember:
The
contrapositive is the mixing of the inverse and the converse. 

