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A set A is a subset of set B if every element of A is also an element of B; e.g. {2, 4} is a subset of {2, 4, 6}

The set that contains all the objects under consideration for a particular discussion; e.g. if discussing natural numbers, the universal set could be the set of all natural numbers.

Two sets are disjoint if they have no elements in common; e.g. {1, 2} and {3, 4} are disjoint sets.

A set with no elements; e.g. {}, denoted by $\emptyset$ or $\varnothing$

The union of sets A and B is the set of elements that are in A, B, or both; e.g. if A = {1, 2} and B = {2, 3}, A U B = {1, 2, 3}

A set with a countable number of elements; e.g. {0, 1, 2, 3, 4, 5} is a finite set with 6 elements.

The set of all subsets of set S, including the empty set and S itself; e.g. if S = {1, 2}, Power set of S: {{}, {1}, {2}, {1, 2}}

A collection of distinct objects; e.g. the set of all even numbers: {2, 4, 6, ...}

The complement of set A is the set of elements in the universal set U that are not in A; e.g. U = {1, 2, 3, 4}, A = {2, 3}, A' = {1, 4}

The number of elements in a set; e.g. if A = {2, 4, 6}, the cardinality of A, denoted as |A|, is 3.

The intersection of sets A and B is the set of elements that are both in A and B; e.g. A = {1, 2, 3}, B = {2, 3, 4}, A ∩ B = {2, 3}

An object or item that is contained within a set; e.g. in the set {a, b, c}, 'a' is an element of the set.

A set A is a proper subset of set B if A is a subset of B and A is not equal to B; e.g. {2} is a proper subset of {2, 4}

The Cartesian product of sets A and B is the set of all ordered pairs (a, b) where a is in A and b is in B; e.g. A = {1, 2}, B = {3, 4}, A x B = {(1, 3), (1, 4), (2, 3), (2, 4)}