Sets: Playing Cards

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# Sets: Playing Cards - PowerPoint PPT Presentation

Sets: Playing Cards Daniel Hunnicutt Set Definition A set is an unordered collection of objects usually denoted by S = { } Playing Card Set (P): {4 of clubs, Ace of Hearts, …} Cardinality (number of elements): 52 Member element S = {a, b, c, …} Membership: a  P Subsets

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Sets: Playing Cards

Daniel Hunnicutt

Set Definition
• A set is an unordered collection of objects usually denoted by S = { }
• Playing Card Set (P):

{4 of clubs, Ace of Hearts, …}

Cardinality (number of elements): 52

Member element S = {a, b, c, …}

Membership: a  P

Subsets
• A subset is any set that is contained within the original set

i.e. Subset Facecards = {King of clubs, …}

Facecards  P

Subset Diamonds ={2 of diamonds,…}

Diamonds  P

• Power set: The set of all subsets of P

i.e. P(P) = { {}, {2 of Hearts}, …}

Connectivity , , -, c
• Diamonds  Facecards:

{Jack of Diamonds, Queen of D, King of D, Ace of D}

• Diamonds  Facecards:

Any Diamond or Facecard {King of clubs, 2 of diamonds,…}

• Diamonds c: {all cards not Diamond}
• Facecards – Diamonds:

{all facecards that are not diamonds}

Partitions
• A partition of a set P is a set of nonempty subsets of P such that every element c in P is in exactly one of these subsets.
• Example: Partition of Suits