Table of Contents
What do you call 2 sets if they contain exactly the same elements?
Equal Sets – Two sets that contain exactly the same elements, regardless of the order listed or possible repetition of elements.
Can a set have two same elements?
A set remains the same if its elements are allegedly repeated or rearranged. As such, the programming languages I know would not put an element into a set if the element already belongs to it, or they would replace it if it already exists, but would never allow a duplication.
What operation of set with elements that are members of both sets combined together?
The set operations are union, intersection, and complement: The union of two sets A and B asks for all the elements in sets A and B — all of them together (without repeating any elements that they share).
Does order matter in sets?
The order of elements in the set does not matter. In general, two sets are the same if and only if they have exactly the same members.
How do you show two sets have the same cardinality?
13.1 Sets with Equal Cardinalities We begin with a discussion of what it means for two sets to have the same cardinality. Up until this point we’ve said |A|=|B| if A and B have the same number of elements: Count the elements of A, then count the elements of B. If you get the same number, then |A|=|B|.
What set operation containing all elements common to the two sets?
The union of a set
The union of a set refers to the collection of all elements that can be found in either of the sets being combined.
Are sets in different orders equal?
Two ordered sets with the same elements are identical as sets; they are not identical as ordered sets if the orders are different (that sounds very tautological).
Can equal sets be equivalent sets?
Yes, all equal sets are also equivalent sets. Equal sets have the exact same elements, so they must have the same number of elements. Therefore, equal sets must also be equivalent.