67 lines
1.5 KiB
Markdown
67 lines
1.5 KiB
Markdown
# Lists
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- Ordered
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- Denoted by (a1, a2, … an) or {a1, a2, …an}
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# Strings and Queues
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## Strings
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- Ordered list
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- (1,2,3,4) or {1,2,3,4}
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## Queue
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- Special list, where elements are removed from the bottom, and added to the top.
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# Sets, Elements
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- Any collection of objects is a set
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- Objects contained in a set are elements, or members
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- Set defined with braces.
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- Conventional to use singular capital letters for names of sets.
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- Commonly denoted a `a ∈ S`, where `a` is an element of the set `S`.
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- Elements that are not contained are denoted as `d ∉ S`, where `d` is not an element of the set `S`.
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## #Cardinality
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- Cardinality of a set is the number of elements contained in the set.
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- For example, let S = {a,b,c}, the cardinality of S is 3.
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- These facts are denoted symbolically
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- n(S) = 3.
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## Set Equality
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- Two sets are equal if they contain exactly the same elements.
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## #Subsets
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- Suppose V is a set, and W is a set formed using only elements of V.
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- W would be a **subset** of V
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- Denoted as `W ⊆ V`, where W is the subset of V
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- Every set is a subset of itself.
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- {Moe, Larry} $\subseteq$ {Moe, Larry}
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- The empty set is a subset of every set .
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- {} $\subseteq$ {Moe, Larry}
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### Example
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Let T = {Moe, Larry, Curly}
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List all subsets of T.
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{Moe}
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{Larry}
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{Curly}
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{Moe, Larry}
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{Moe, Curly}
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{Larry, Curly}
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{Moe, Larry, Curly}
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{} <- Empty Set
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## True or False
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1. {b, h, r, q} $\subseteq$ {h, r} - True
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2. {a, 13, d, 2} $\subseteq$ {13, 2, d, a} - True
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