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First of all, the null set( denoted by is a subset of every set. But it being a proper set or improper set is debatable. Many mathematicians regard it as an improper set, and rightly have as when we say a set is a subset of another, the super set always contains at least one element. For eg,.

Let A be the set, in roster form we take it as:

A = {ϕ}, we clearly see n(A)=1

then P(A) = {ϕ,{ϕ}}

We observe that at least a set must have 1 element for it to have a proper set, but if we take A = ϕ ( i.e. n(A)=0), then clearly ϕ and A itself are improper sets of A and.

Hence the minimum amount of proper sets a set has is nil and improper is 2.

But I have seen a few high school text books who regard null set as a proper set, which is totally false, arguable by mathematicians, clearly signifying the lethargy of authors of the book failing to update their error driven books.

I assure you, that null set is an improper set of every set.

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Q: Is null set proper subset of every set?

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No. The null set cannot have a proper subset. For any other set, the null set will be a proper subset. There will also be other proper subsets.

The null set. Every set is a subset of itself and so the null set is a subset of the null set.

It's an axiom.

Yes the null set is a subset of every set.

The null set. It is a subset of every set.

yes

yes!

The definition of subset is ; Set A is a subset of set B if every member of A is a member of B. The null set is a subset of every set because every member of the null set is a member of every set. This is true because there are no members of the null set, so anything you say about them is vacuously true.

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.

A set with only one element in it. The only proper subset of such a set is the null set.

The null set is a proper subset of any non-empty set.

The only proper subset of a set comprising one element, is the null set.

It isn't. The empty set is a subset - but not a proper subset - of the empty set.

No, but it is a subset of every set.It is an element of the power set of every set.

Because every set is a subset of itself. A proper subset cannot, however, be a proper subset of itself.

It is a proper subset of every set other than itself. Its cardinality (size) is 0. It is unique (the only set with no elements).

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.

Yes. One of the subsets is the set itself. The other is the null 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 is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.An empty set is not a proper subset of an empty set.

Yes. A null set is always a subset of any set. Also, any set is a subset of the [relevant] universal set.

A set "A" is said to be a subset of of set "B", if every element in set "A" is also an element of set "B". If "A" is a subset of "B" and the sets are not equal, "A" is said to be a proper subset of "B". For example: the set of natural numbers is a subset of itself. The set of square numbers is a subset (and also a proper subset) of the set of natural numbers.

Yes,empty set or void set or null set is a subset of every set.In order to know the number of subsets of any set, first of all count the number of elements in the set and take the number of elements as the exponent of 2, then you will get the number of subsets of any set.

NO- by definition a set is not a proper subset of itself . ( It is a subset, but not a proper one. )

Yes.