|
|
|
Viewing Version
3
of
'contrapositive'
|
[ view 'contrapositive'
|
back to history
]
| Title of object: |
contrapositive |
| Canonical Name: |
Contrapostive |
| Type: |
Definition |
| Created on: |
2001-11-16 10:38:27 |
| Modified on: |
2002-08-30 15:01:32 |
| Classification: |
msc:03B05 |
Revision comment (for changes between this and next version):
Preamble:
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{graphicx}
\usepackage{xypic} |
Content:
Given an implication of the form
$$p \implies q$$
("p implies q") the \emph{contrapositive} of this implication is
$$\overline{q} \implies \overline{p}$$
("not q implies not p").
An implication and its contrapositive are equivalent statements. When proving a theorem, it is often more convenient or more intuitive to prove the contrapositive instead. |
|
|
|
|
|
