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A tree is a connected graph with no cycles. Properties include having exactly $n-1$ edges for $n$ vertices, and any two vertices are connected by exactly one path.

An algorithm is a finite sequence of well-defined instructions, typically used to solve a class of problems or perform a computation. Properties include runtime complexity and space complexity.

A set is a well-defined collection of distinct objects. Set properties include cardinality, subsets, intersections, unions, and complements.

A graph is an ordered pair $G = (V, E)$ where $V$ is a set of vertices and $E$ is a set of edges, which are 2-element subsets of $V$. Properties include connectivity, cycles, and possibly directed or weighted edges.

A combination is a selection of items from a collection, such that the order of selection does not matter. Given $n$ elements and selecting $r$ at a time, the number of combinations is $C(n, r) = \frac{n!}{r!(n-r)!}$.

A matrix is a rectangular array of numbers, symbols, or expressions, arranged in rows and columns. Properties include determinant, rank, and can represent systems of linear equations.

Recursion is a method where the solution to a problem depends on solutions to smaller instances of the same problem. A recursive function calls itself with a smaller input.

A relation between two sets is a collection of ordered pairs containing one object from each set. Properties include reflexive, symmetric, transitive, and equivalence relations.

A function $f$ from a set $X$ to a set $Y$ assigns each element of $X$ to exactly one element of $Y$. Properties include being one-to-one (injective), onto (surjective), or both (bijective).

A binary tree is a tree in which each node has at most two children, which are referred to as the left child and the right child. Properties include height, balance, and it is the basis for binary search trees.

A lattice is a partially ordered set (poset) in which any two elements have a unique supremum (the elements' least upper bound; called their join) and an infimum (greatest lower bound; called their meet).