Set & Set Notation

Set

A collection of elements.

Element

An individual object in a set.

Member

Another word for an element of a set.

Listing rule

Writing a set by listing all its elements, e.g. A = {1, 2, 3}.

n(A)

Number of elements in set A.

x ∈ A

x is a member (element) of set A.

x ∉ A

x is not a member (element) of set A.

∅

The empty set (no elements).

U

The universal set (all possible elements in the context).

A = B

Sets A and B are equal (contain the same elements).

A ⊆ B

A is a subset of B (all elements of A are in B).

A ⊂ B

A is a proper subset of B (subset but not equal).

A ∩ B

Intersection: elements in both A and B.

A ∪ B

Union: elements in A or B or both.

A \ B

Elements in A but not in B.

A′

The complement of A: elements not in A.

(A ∪ B)′

Elements in neither A nor B.

(A ∩ B)′

Elements not in both A and B.

P(A)

Probability of event A.

P(A′)

Probability of the complement of A.

P(A ∪ B)

Probability of A or B.

P(A ∩ B)

Probability of A and B.

P(A | B)

Conditional probability: probability of A given B.

Independent events

Two events where P(A ∩ B) = P(A)P(B).

Mutually exclusive events

Events that cannot both occur: P(A ∩ B) = 0.

Sample space

The set of all possible outcomes.

Outcome

One possible result of a random experiment.

Random variable

A variable whose value is determined by a random process.

X

A random variable (typically discrete in AS).

x

A possible value of X.

P(X = x)

The probability that random variable X takes the value x.

Σ

Summation symbol (used for expected value).

E(X)

Expectation (mean) of a random variable X.

Var(X)

Variance of X.