If all elements of set A are also elements of set B, then set A is a subset of set B.
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A SUBSET!!!
e.g.
ABCBCCCBBDD is a set. A subset would say all the 'D'.
ABCBCCCBB (DD)
A relationship is a way of associating members of one set to members of another set (the two sets could be the same). The first of these sets is the domain and the second is the range.
That is called the UNION of the two sets.
No, they do not.
The collection of all sets minus the empty set is not a set (it is too big to be a set) but instead a proper class. See Russell's paradox for why it would be problematic to consider this a set. According to axioms of standard ZFC set theory, not every intuitive "collection" of sets is a set; we must proceed carefully when reasoning about what is a set according to ZFC.
The universal set is represented by a rectangle. Subsets of this set are represented by closed curves (often circles). A ⊂ € Further subsets are represented by a closed curve within a larger closed curve. Q ⊂ P ⊂ € The intersection of two sets (A & B) is the set of elements that are members of both A & B and is usually shown as a shaded region. A ∩ B The union of two sets (A & B) is the set of all elements contained in A & B. A ∪ B.