Set Theory Vocabulary Worksheet

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All 36 terms

Core terms 12

cardinality The number of elements in a set. The cardinality of {2, 4, 6} is 3.
complement Everything in the universal set that is not in a given set. In the universal set {1, 2, 3, 4, 5}, the complement of {1, 2} is {3, 4, 5}.
disjoint Having no element in common with another set. {1, 2} and {3, 4} are disjoint: their intersection is empty.
element One of the objects that belong to a set. 4 is an element of {2, 4, 6}. An element is also called a member.
empty set The set that has no elements at all. It is written { } or ∅. The set of odd numbers in {2, 4, 6} is empty.
intersection The elements that two sets have in common. The intersection of {1, 2} and {2, 3} is {2}.
set A collection of distinct objects, taken as one whole. {2, 4, 6} is a set of three numbers.
set theory The branch of mathematics that studies sets. Union and intersection are two of its operations.
subset A set whose every element also lies in another set. {2, 4} is a subset of {2, 4, 6}.
union All the elements that are in at least one of two sets. The union of {1, 2} and {2, 3} is {1, 2, 3}.
universal set The set of all objects under discussion in a problem. For a problem about the whole numbers 1 to 10, that list is the universal set.
Venn diagram A picture of sets as overlapping circles or other shapes. Two overlapping circles show two sets. The overlap is their intersection.

Show all 36 terms (24 more)

Kinds of sets and notation 12

brace Either of the curly marks { } put around a list of elements. The braces in {2, 4, 6} show that the list is a set.
ellipsis A row of dots showing that a pattern continues. {1, 2, 3, ...} uses an ellipsis for the whole numbers that follow.
equal sets Two sets that have exactly the same elements. {1, 2, 3} and {3, 2, 1} are equal sets: the order of a list does not matter.
finite set A set with a limited number of elements. The set of days of the week is finite: it has 7 elements.
infinite set A set whose elements go on without end. The counting numbers 1, 2, 3 and so on form an infinite set.
partition A split of a set into non-empty parts that do not overlap. {1, 2}, {3} and {4, 5} make a partition of {1, 2, 3, 4, 5}.
power set The set of all the subsets of a set. The power set of {1, 2} is {{ }, {1}, {2}, {1, 2}}: 4 subsets.
proper subset A subset that is not the whole set itself. {2, 4} is a proper subset of {2, 4, 6}. {2, 4, 6} is a subset of itself, but not a proper one.
roster notation Writing a set as a list of its elements inside braces. {a, e, i, o, u} is the set of vowels in roster notation.
set-builder notation Describing a set by a rule its elements must satisfy. {x | x is an even number} is read: the set of all x such that x is an even number.
singleton A set that holds one element and no more. {7} is a singleton.
superset A set that holds every element of another set. {2, 4, 6} is a superset of {2, 4}.

Operations, pairs and functions 12

bijection A function that matches two sets up with none left over. Between {1, 2, 3} and {a, b, c}, sending 1 to a, 2 to b and 3 to c is a bijection.
Cartesian product The set of all ordered pairs taken from two sets. For {1, 2} and {a, b} it is {(1, a), (1, b), (2, a), (2, b)}.
De Morgan's laws Two rules for the complement of a union or an intersection. The complement of a union is the intersection of the complements, and the complement of an intersection is the union of the complements.
domain The set of first elements in a function's pairs. The domain of {(1, 2), (2, 4), (3, 6)} is {1, 2, 3}: the inputs.
function A relation with exactly one pair for each first element. {(1, 2), (2, 4), (3, 6)} is a function: each input, 1, 2 or 3, has one output, its double.
injection A function in which no two pairs share a second element. Doubling is an injection on the whole numbers. It is also called a one-to-one function.
ordered pair Two objects in a fixed order, written (a, b). (1, 2) and (2, 1) are different ordered pairs.
range The set of second elements in a function's pairs. The range of {(1, 2), (2, 4), (3, 6)} is {2, 4, 6}: the outputs. It is also called the image.
relation A subset of a Cartesian product: a choice of its pairs. {(1, 2), (1, 3), (2, 3)} is the relation "is less than" on {1, 2, 3}.
set difference The elements of one set that are not in a second set. {1, 2, 3} minus {2, 3, 4} is {1}. It is also called the relative complement.
surjection A function that reaches every element of its target set. From {1, 2, 3} to {a, b}, a function that reaches both a and b is a surjection. It is also called an onto function.
symmetric difference The elements that are in exactly one of two sets. For {1, 2, 3} and {2, 3, 4} it is {1, 4}.

How this list was compiled: Term list chosen for this site on 2026-10-09. Each meaning is written in our own words and was checked that day against the articles Set (mathematics), Infinite set, Function (mathematics) and Binary relation in English Wikipedia (https://en.wikipedia.org/), whose text is under the Creative Commons Attribution-ShareAlike license, and, as a second reference, against the entry for the term in Wiktionary, the free dictionary (https://en.wiktionary.org/), under the same license. Two terms have no dictionary entry and rest on the article Set (mathematics) alone: roster notation (its section Roster notation) and equal sets (its sentence on when two sets are equal). Infinite set was read in the article Infinite set and in the dictionary's entry for infinite. Every example was worked out and checked a second time. The example after each meaning is our own. Licence: own work

How it works

Twelve terms run down the left of this set theory vocabulary worksheet and their meanings, in another order, down the right. It opens on core terms; two more sets hold kinds of sets and notation, and operations, pairs and functions.

Read the full guide

Core terms, then kinds of sets

Set opens on Core terms: set theory, set, element, subset, empty set, universal set, union, intersection, complement, disjoint, Venn diagram and cardinality. Kinds of sets and notation prints singleton, finite set, infinite set, equal sets, proper subset, superset, power set, partition, roster notation, set-builder notation, brace and ellipsis.

Operations, pairs and functions

The third of these set theory vocabulary worksheets goes further: set difference, symmetric difference, De Morgan's laws, ordered pair, Cartesian product, relation, function, domain, range, injection, surjection and bijection. Under the tool each term has a small example, most of them written in braces.

The meanings on the sheet are in words: no union, intersection or element sign is printed.

Questions and answers

What is the difference between union and intersection?

The union of two sets holds every element that is in at least one of them. The intersection holds only the elements in both. For {1, 2} and {2, 3} the union is {1, 2, 3} and the intersection is {2}.

What is the difference between a subset and a proper subset?

A subset is a set whose elements all belong to a given set, so every set is a subset of itself. A proper subset is not the whole set: {2, 4} is a proper subset of {2, 4, 6}.

What is the complement of a set?

Everything in the universal set that is not in the set. If the universal set is {1, 2, 3, 4, 5}, the complement of {1, 2} is {3, 4, 5}.

What does cardinality mean?

The cardinality of a set is the number of elements in it. The set {2, 4, 6} has cardinality 3, and the empty set has cardinality 0.

All 36 terms

Core terms 12

Kinds of sets and notation 12

Operations, pairs and functions 12

How it works

Core terms, then kinds of sets

Operations, pairs and functions

Questions and answers

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