Set theory

1. Subset A set A is said to be a proper subset of a set B if every element of A is also an element of B, and there exists at least one element in B that is not in A.
5. Product The Cartesian product of two sets A and B is the set of all ordered pairs (a, b) where a is an element of A and b is an element of B.
7. The intersection of two sets A and B is the set that contains all the elements that are common to both A and B.
9. Sets Two sets are said to be disjoint if they have no elements in common.
11. Set The empty set, denoted by ∅ or {}, is the set that contains no elements.
13. Set The universal set is the set that contains all the objects under consideration in a particular context.
15. The complement of a set A with respect to a universal set U is the set that contains all the elements in U that are not in A.

2. Set The power set of a set A is the set that contains all possible subsets of A, including the empty set and the set itself.
3. The cardinality of a set is the number of elements in the set.
4. The union of two sets A and B is the set that contains all the elements that are in A or B (or both).
6. Difference The set difference of two sets A and B is the set that contains all the elements that are in A but not in B.
8. Equality Two sets A and B are said to be equal if every element of A is also an element of B and every element of B is also an element of A.
10. A set A is said to be a subset of a set B if every element of A is also an element of B.
12. An individual object that belongs to a set.
14. A collection of distinct objects, called elements, that are considered as a whole.