3.5 KiB
| title | TARGET DECK | FILE TAGS | tags | ||
|---|---|---|---|---|---|
| Algebra of Sets | Obsidian::STEM | algebra::set set |
|
Overview
The study of the operations of union (\cup), intersection (\cap), and set difference (-), together with the inclusion relation (\subseteq), goes by the algebra of sets.
%%ANKI
Basic
What three operators make up the algebra of sets?
Back: \cup, \cap, and -.
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
%%ANKI
Basic
What relation is relevant in the algebra of sets?
Back: \subseteq
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
Laws
The algebra of sets obey laws reminiscent (but not exactly) of the algebra of real numbers.
%%ANKI
Cloze
{\cup} is to algebra of sets whereas {+} is to algebra of real numbers.
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
%%ANKI
Cloze
{\cap} is to algebra of sets whereas {\cdot} is to algebra of real numbers.
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
%%ANKI
Cloze
{-} is to algebra of sets whereas {-} is to algebra of real numbers.
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
%%ANKI
Cloze
{\subseteq} is to algebra of sets whereas {\leq} is to algebra of real numbers.
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
Commutative Laws
For any sets A and B, \begin{align*} A \cup B & = B \cup A \ A \cap B & = B \cap A \end{align*}
%%ANKI
Basic
The commutative laws of the algebra of sets apply to what operators?
Back: \cup and \cap
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
%%ANKI
Basic
What does the union commutative law state?
Back: For any sets A and B, A \cup B = B \cup A.
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
%%ANKI
Basic
What does the intersection commutative law state?
Back: For any sets A and B, A \cap B = B \cap A.
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
Associative Laws
For any sets A and B, \begin{align*} A \cup (B \cup C) & = (A \cup B) \cup C \ A \cap (B \cap C) & = (A \cap B) \cap C \end{align*}
%%ANKI
Basic
The associative laws of the algebra of sets apply to what operators?
Back: \cup and \cap
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
%%ANKI
Basic
What does the union associative law state?
Back: For any sets A, B, and C, A \cup (B \cup C) = (A \cup B) \cup C.
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
%%ANKI
Basic
What does the intersection associative law state?
Back: For any sets A, B, and C, A \cap (B \cap C) = (A \cap B) \cap C.
Reference: Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).
END%%
Bibliography
- Herbert B. Enderton, Elements of Set Theory (New York: Academic Press, 1977).