Sets and Relations

A set is a collection

A set is a collection of well-defined objects. Three main representation methods: Roster method lists all elements {1,2,3}, Set-builder method describ

Empty set (φ) contains no elements

Empty set (φ) contains no elements, Singleton set has exactly one element, Finite sets have countable elements, Infinite sets have uncountable element

Union (A∪B) combines all elements

Union (A∪B) combines all elements, Intersection (A∩B) finds common elements, Complement (A') contains elements not in A, Difference (A-B) has elements

n(A∪B) = n(A) + n(B)

n(A∪B) = n(A) + n(B) - n(A∩B) for two sets. For three sets: n(A∪B∪C) = n(A) + n(B) + n(C) - n(A∩B) - n(B∩C) - n(A∩C) + n(A∩B∩C). Problem-solving appro

Open interval (a

Open interval (a,b) excludes endpoints, Closed interval [a,b] includes endpoints, Semi-open [a,b) or (a,b] includes one endpoint. Infinite intervals u