RosettaCodeData/Task/Set/00DESCRIPTION

{{data structure}}
A   '''set'''  is a collection of elements, without duplicates and without order.


;Task:
Show each of these set operations:

* Set creation
* Test m ∈ S -- "m is an element in set S"
* A ∪ B -- ''union''; a set of all elements either in set A or in set B.
* A ∩ B -- ''intersection''; a set of all elements in ''both'' set A and set B.
* A ∖ B -- ''difference''; a set of all elements in set A, except those in set B.
* A ⊆ B -- ''subset''; true if every element in set A is also in set B.
* A = B -- ''equality''; true if every element of set A is in set B and vice versa.

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As an option, show some other set operations.
<br>(If A &sube; B, but A &ne; B, then A is called a true or proper subset of B, written A &sub; B or A &#x228a; B.)

As another option, show how to modify a mutable set.


One might implement a set using an [[associative array]] (with set elements as array keys and some dummy value as the values).

One might also implement a set with a binary search tree, or with a hash table, or with an ordered array of binary bits (operated on with bit-wise binary operators).

The basic test, m &isin; S, is [[O]](n) with a sequential list of elements, O(''log'' n) with a balanced binary search tree, or (O(1) average-case, O(n) worst case) with a hash table.


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