Set Theory

What is an element?

A possible outcome of an experiment.

What is a set?

A collection of zero or more elements. We denote a set using an uppercase letter. The elements of the set are typically written as lowercase letters and separated by commas.

What is a Venn Diagram?

A diagram showing the relationship between a finite number of sets. Venn diagrams are useful to illustrate probabilities and events.

What is a Sample Space?

The collection of all possible outcomes. It is usually denoted by an uppercase S.

What is an Empty Set?

An empty set is a set containing zero elements. This is denoted by ∅ or {}.

What is an Event?

An event is a subset of the sample space. In short, events and sets are interchangeable, where an event is typically described in words.

What is a Subset?

A set, D , is the subset of a set, E , if all the elements in D are also in set E. We allow for the possibility that D = E. In set notation, this relationship is expressed as D ⊂ E.

What is a Union?

The union of multiple sets is the set of all elements that are contained in at least one of the sets.

What is an Intersection?

The intersection of multiple sets is the set of elements that are common for each set.

What does Difference mean?

The difference between set F and set G is the set containing all elements that are in F but not in G. It is denoted by F - G.

What does Mutually Exclusive mean?

Two sets, M and N, are mutually exclusive if they share no common elements. This implies that the intersection between M and N is the empty set, i.e. M ∩ N = ∅

What does Disjoint mean?

The term "disjoint" has the same meaning as the term "mutually exclusive."

What does Complement mean?

The complement of a set, T , is the set containing all of the elements in the sample space except the elements that are in T. The complement of is denoted by T' or Tᶜ.