# Lists

- Ordered
- Denoted by (a1, a2, … an) or {a1, a2, …an}

# Strings and Queues

## Strings

- Ordered list
- (1,2,3,4) or {1,2,3,4}

## Queue

- Special list, where elements are removed from the bottom, and added to the top.

# Sets, Elements

- Any collection of objects is a set
- Objects contained in a set are elements, or members
- Set defined with braces.
- Conventional to use singular capital letters for names of sets.
- Commonly denoted a `a ∈ S`, where `a` is an element of the set `S`.
	- Elements that are not contained are denoted as `d ∉ S`, where `d` is not an element of the set `S`.

## #Cardinality

- Cardinality of a set is the number of elements contained in the set.
- For example, let S = {a,b,c}, the cardinality of S is 3.
- These facts are denoted symbolically
	- n(S) = 3.

## Set Equality

- Two sets are equal if they contain exactly the same elements.

## #Subsets

- Suppose V is a set, and W is a set formed using only elements of V.
	- W would be a **subset** of V
- Denoted as `W ⊆ V`, where W is the subset of V
- Every set is a subset of itself.
	- {Moe, Larry} $\subseteq$ {Moe, Larry}
- The empty set is a subset of every set .
	- {} $\subseteq$ {Moe, Larry}

### Example

Let T = {Moe, Larry, Curly}

List all subsets of T.

{Moe}
{Larry}
{Curly}
{Moe, Larry}
{Moe, Curly}
{Larry, Curly}
{Moe, Larry, Curly}

{} <- Empty Set

## True or False

1. {b, h, r, q} $\subseteq$ {h, r} - True
2. {a, 13, d, 2} $\subseteq$ {13, 2, d, a} - True