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A collection of distinct objects, considered as an object in its own right. Example: The set of all even numbers.

A relation that uniquely associates each element of a set with exactly one element of another set. Example: $f(x) = x^2$ is a function that maps every real number x to its square.

A collection of vertices connected by edges. Example: A simple graph with vertices {A, B, C} and edges {AB, AC, BC}.

A subset of the Cartesian product of two sets. Example: The 'less than' relation, <$, on the set of integers.$

An arrangement of all or part of a set of objects, with regard to the order of arrangement. Example: The permutations of the set {1,2,3} are {123,132,213,231,312,321}.

A selection of items from a larger set, such that the order of selection does not matter. Example: From the set {a,b,c}, the combinations of 2 are {ab, ac, bc}.

A declarative statement that is either true or false but not both. Example: 'The Eiffel Tower is in Paris' is a proposition.

A table that shows the truth value of a logical expression based on the truth values of its components. Example: The truth table for AND operation between two variables A and B.

An operator that connects propositions to create a new proposition. Example: AND (∧), OR (∨), NOT (¬).

A principle stating that if $n$ items are put into $m$ containers, with $n > m$, then at least one container must contain more than one item. Example: Placing 10 pigeons in 9 pigeonholes.

A relation that is defined in terms of itself. Example: The Fibonacci sequence $F(n) = F(n-1) + F(n-2)$.

A binary relation that is reflexive, symmetric, and transitive. Example: The equality relation '=' on the set of integers.

A correspondence between two graphs that maps vertices to vertices and edges to edges, preserving adjacency. Example: Two graphs with the same vertices and edges layout but different labeling.

A graph that can be drawn on a plane without any edges crossing. Example: A graph with 5 vertices and 7 edges that can be drawn without any crossing lines.

A path in a graph that visits each vertex exactly once. Example: A route that visits every city in a list without repetition.

A closed path in a graph that uses every edge exactly once. Example: A mail carrier's route that crosses every bridge in a city once and returns to the starting point.

A branch of algebra that deals with true or false values and logical operations. Example: The expression $(T ∨ F) ∧ T$ evaluates to true.

The set of all ordered pairs obtained by taking each element of one set and pairing it with each element of another set. Example: The Cartesian product of sets A = {x,y} and B = {1,2} is A×B = {(x,1), (x,2), (y,1), (y,2)}.

A graph in which the edges have a direction associated with them. Example: A graph representing a one-way street system between intersections.