Cartesian product (original) (raw)
The Cartesian product satisfies the following properties, for all sets A, B, C, and D:
- •
A×∅=∅ - •
(A×B)∩(C×D)=(A∩C)×(B∩D) - •
(A×B)∁=(A∁×B∁)∪(A∁×B)∪(A×B∁)
Here ∅ denotes the empty set
, ∩ denotes intersection
, ∪ denotes union, and ∁ denotes complement with respect to some universal set U containing A and B.
| Title | Cartesian product |
|---|---|
| Canonical name | CartesianProduct |
| Date of creation | 2013-03-22 11:48:56 |
| Last modified on | 2013-03-22 11:48:56 |
| Owner | djao (24) |
| Last modified by | djao (24) |
| Numerical id | 10 |
| Author | djao (24) |
| Entry type | Definition |
| Classification | msc 03-00 |
| Classification | msc 81P10 |
| Classification | msc 81P05 |
| Related topic | GeneralizedCartesianProduct |