Concept
Why do a set and its complement form a partition?
Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk / Chapter 1
"Every set (S) together with its (total) complement (S) forms a partition of the entire domain of discourse Ω. This is because every element either is, or is not, in any given set. The set of males and non-males are a partition of Ω because everything is either a male or a non-male, and never both (inanimate objects and other nouns are non-males, just as women are). The set of prime numbers and the set of everything-except-prime-numbers are a partition. The set of underdone cheeseburgers and the set of everything-except-underdone-cheeseburgers form a partition of Ω. By pure logic, this is true no matter what the set is."
Related Ideas
- How do partitions divide an event into mutually exclusive and exhaustive pieces?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- Do { Matthew, Mark, Luke } and { John } form a partition of G?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- Are {Mark, Luke} and {Matthew, Luke} a partition of G?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How do membership symbols and fuzzy sets change the idea of belonging?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How are sets written, and what are empty and domain sets?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How do sets differ from arrays and linked lists in order and duplication?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- How do De Morgan’s laws relate complements to unions and intersections?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1
- What laws describe how union and intersection combine sets?Stephen Davies, Ph.D. Version 2.2.2 Through Discrete Mathematics A Cool Brisk Walk · Chapter 1