# Context: proveit.logic.set_theory¶

Basic set theory context dealing with membership (e.g., $x \in S$), enumeration (e.g., $\{e_1, e_2, e_3\}$), containment (e.g., $A \subseteq B$), unification (e.g., $A \cup B \cup C$), intersection (e.g., $A \cap B \cap C$), subtraction (e.g., $A - B$), comprehension (e.g., $\{f(x)~|~Q(x)\}_{x \in S}$), and cardinatly (e.g., $|S|$).

In [1]:
import proveit
%context

common expressions axioms theorems demonstrations
membership Is an element a member of a set? Not a member of a set? Define a set by enumerating its contents. Is one set contained by another? Define a set as the union of sets. Define a set as the intersection of sets. Define a set by removing elements from an original set. Define a set according to the properties of its members. Are their common elements between sets? Also defines "distinct". How large is a set?