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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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Why a null set is subst of every set?
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.
Is the null set an element of every set?
No, but it is a subset of every set.It is an element of the power set of every set.
Can any set be a proper set of itself?
NO- by definition a set is not a proper subset of itself . ( It is a subset, but not a proper one. )
Why null set is not considered as an element of any set even though it is an subset of every set?
Let set A = { 1, 2, 3 } Set A has 3 elements. The subsets of A are {null}, {1}, {2}, {3}, {1,2},{1,3},{1,2,3} This is true that the null set {} is a subset. But how many elements are in the null set? 0 elements. this is why the null set is not an element of any set, but a subset of any set. ====================================== Using the above example, the null set is not an element of the set {1,2,3}, true. {1} is a subset of the set {1,2,3} but it's not an element of the set {1,2,3}, either. Look at the distinction: 1 is an element of the set {1,2,3} but {1} (the set containing the number 1) is not an element of {1,2,3}. If we are just talking about sets of numbers, then another set will never be an element of the set. Numbers will be elements of the set. Other sets will not be elements of the set. Once we start talking about more abstract sets, like sets of sets, then a set can be an element of a set. Take for example the set consisting of the two sets {null} and {1,2}. The null set is an element of this set.
What is an example of a proper subset?
Let A be the set {1,2,3,4} B is {1,2} and B is a proper subset of A C is {1} and C is also a proper subset of A. B and C are proper subsets of the set A because they are strictly contained in A. necessarily excludes at least one member of A. The set A is NOT a proper subset of itself.
Does every set have a proper subset?
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.
What is the subset of null set?
The null set. Every set is a subset of itself and so the null set is a subset of the null set.
Proof is null set proper subset of every set?
It's an axiom.
Is a null set in mathematics a subset of every set?
Yes the null set is a subset of every set.
What is universal subset?
The null set. It is a subset of every set.
Every subset of a null set is a null set?
yes
Is null set a proper subset?
yes!
Why a null set is subst of every set?
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.
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.
Which set possesses only one proper subset?
A set with only one element in it. The only proper subset of such a set is the null set.
What are the proper subsets of 36912 in matrix form?
The only proper subset of a set comprising one element, is the null set.
Is a nullset a proper subsets?
The null set is a proper subset of any non-empty set.
