Difference between revisions of "Contrapositive"

 
(See also)
 
(3 intermediate revisions by 3 users not shown)
Line 3: Line 3:
 
A [[conditional]] statement is usually expressed as
 
A [[conditional]] statement is usually expressed as
  
If '''P''', then '''Q'''
+
If '''P''', then '''Q'''.
  
 
The contrapositive statement is usually expressed as
 
The contrapositive statement is usually expressed as
  
If not '''Q''', then not '''P'''
+
If not '''Q''', then not '''P'''.
  
 
where '''P''' denotes a condition and '''Q''' denotes another condition.
 
where '''P''' denotes a condition and '''Q''' denotes another condition.
Line 14: Line 14:
  
 
Given the conditional statement "If a polygon has 3 sides, then it is a triangle", the contrapositive is "If a polygon is not a triangle, then it does not have 3 sides".
 
Given the conditional statement "If a polygon has 3 sides, then it is a triangle", the contrapositive is "If a polygon is not a triangle, then it does not have 3 sides".
 +
 +
== See also ==
 +
* [[Logic]]

Latest revision as of 13:08, 19 December 2016

A contrapositive of a statement is always true, assuming that the conditional statement is true. However, if the conditional statement is false, then the contrapositive is also false.

A conditional statement is usually expressed as

If P, then Q.

The contrapositive statement is usually expressed as

If not Q, then not P.

where P denotes a condition and Q denotes another condition.

Examples

Given the conditional statement "If a polygon has 3 sides, then it is a triangle", the contrapositive is "If a polygon is not a triangle, then it does not have 3 sides".

See also

Invalid username
Login to AoPS