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What is a subset of every set?
The empty set!
Is null set a proper subset of any set?
yes, if the set being described is empty, we can talk about proper and improper subsets. there are no proper subsets of the empty set. the only subset of the empty set is the empty set itself. to be a proper subset, the subset must be strictly contained. so the empty set is an improper subset of itself, but it is a proper subset of every other set.
Why is every set a subset of itself?
That is how "subsets" are defined.
Why empty set or null set is subset of every 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.
What is a proper 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.
