The laws of set algebra, one page each¶
Level: 101 · reference · the ten rows of the table on the algebra of sets, each with its own page
Each page states one law for sets, for logic and in Python, says in a sentence why it is true, names where it is used and the trap next to it, and runs a program that checks the law on every subset of a four-element universe and prints the matching truth table.
| Law | Sets |
|---|---|
| identity | A ∪ ∅ = A, A ∩ U = A |
| domination | A ∪ U = U, A ∩ ∅ = ∅ |
| idempotent | A ∪ A = A, A ∩ A = A |
| complement | A ∪ A′ = U, A ∩ A′ = ∅ |
| double complement | (A′)′ = A |
| commutative, associative | A ∪ B = B ∪ A, (A ∪ B) ∪ C = A ∪ (B ∪ C), and the same for ∩ |
| distributive | A ∩ (B ∪ C) = (A ∩ B) ∪ (A ∩ C), and with ∪ and ∩ swapped |
| absorption | A ∪ (A ∩ B) = A, A ∩ (A ∪ B) = A |
| De Morgan | (A ∪ B)′ = A′ ∩ B′, (A ∩ B)′ = A′ ∪ B′ |
| difference | A ∖ B = A ∩ B′ |
Po polsku, w skrócie¶
Dziesięć praw algebry zbiorów z tabeli na stronie nadrzędnej, każde na osobnej stronie: dla zbiorów, dla logiki i w Pythonie, z jednym zdaniem dlaczego zachodzi, z zastosowaniem i pułapką obok, i z programem, który sprawdza prawo na wszystkich podzbiorach czteroelementowego uniwersum.
Auf Deutsch: Stichwörter¶
Die zehn Gesetze der Mengenalgebra, je eine Seite mit Programm.
Stichwörter: Gesetz (law), Mengenalgebra, Absorption, Kommutativität, Assoziativität, Komplement, De Morgan, Differenz, Distributivität, Idempotenz, neutrales Element.