The set theory is a branch of mathematics that studies collections of objects called sets. The set theory explains nearly all definitions of mathematical objects.
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There is no such thing as a "set of all sets". To be more precise, the idea of a "set of all sets" leads to contradictions; therefore this term is avoided in set theory. Check the Wikipedia article on "Universal set" for more details.
It is used in set theory to indicate intersection. The intersection of two sets, A and B, is the set of all elements that are in A as well as in B.
The unit that deals with sets. Different courses have different names for units so it is not possible to give a definitive answer.
Joint sets are sets that have common element.
I presume you mean intersecting. Two sets are intersecting if they have members in common. The set of members common to two (or more) sets is called the intersection of those sets. If two sets have no members in common, their intersection is the empty set. In this case the sets are called disjoint.