Basics

Question 1

Set

Answer 1

A collection of distinct objects. Example: {1, 2, 3}

Question 2

Union (∪)

Answer 2

Combines all elements from two sets. Example: {1, 2} ∪ {2, 3} = {1, 2, 3}

Question 3

Intersection (∩)

Answer 3

Elements common to two sets. Example: {1, 2} ∩ {2, 3} = {2}

Question 4

Cartesian Product (×)

Answer 4

Set of all ordered pairs from two sets. Example: {a, b} × {1, 2} = {(a, 1), (a, 2), (b, 1), (b, 2)}

Question 5

Relation

Answer 5

A subset of a Cartesian product. Example: R = {(1, 2), (2, 3)} on {1, 2} × {2, 3}

Question 6

Function

Answer 6

relation where each input has exactly one output. Example: f(x) = x²

Question 7

Pigeonhole Principle

Answer 7

If n items are put into m containers, and n > m, at least one container has more than one item.

Question 8

Permutation

Answer 8

Ordered arrangement. Formula: P(n, r) = n! / (n - r)!. Example: P(3, 2) = 6

Question 9

Combination

Answer 9

Unordered selection. Formula: C(n, r) = n! / (r!(n - r)!). Example: C(3, 2) = 3

Question 10

Graph

Answer 10

A set of vertices connected by edges. Example: V = {A, B}, E = {(A, B)}