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.
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Empty set or null set
empty set is a set because its name indicate as it is the set.
There is only one empty set, also known as the null set. It is the set having no members at all. It is a subset of every set, since it has no member that is not a member of any other set.
There is no such concept as "proper set". Perhaps you mean "proper subset"; a set "A" is a "proper subset" of another set "B" if:It is a subset (every element of set A is also in set B)The sets are not equal, i.e., there are elements of set B that are not elements of set A.
an empty set does not have any element