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To me, I believe that a power set is not empty. Here is my thought:
∅ ∊ P(A) where P(A) is the power set and A is the set.
This implies:
∅ ⊆ A
This means that A = ∅, but ∅ ∉ A. ∅ ∊ A if A = {∅} [It makes sense that ∅ ∊ {∅}]. Then, {∅} ⊆ A, so {∅} ∊ P(A) = {∅, {∅}}. That P(A) is not empty since it contains {∅} and ∅.
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What is power set of power set of an empty set?
It is the set comprising the following 4 elements:phi,{phi},{{phi}} and{phi, {phi}}
Is power set of singleton set equal to null set?
No. Let A = {a} (a singleton set) then P(A) = {a, 0} where 0 is the null (empty) set.
Is an empty set a subset of every set?
Yes,an empty set is the subset of every set. The subset of an empty set is only an empty set itself.
What isan empty set?
The empty set is a set that has no elements.
What will be the representation of subset of a empty set?
The only subset of an empty set is the empty set itself.
What is the power set of an empty set?
The power set of the empty has one member, which is the set whose member is the empty set . {phi} ( Actually the symbol for the empty set is the Norwegian letter O which resembles the Greek letter phi but is a different symbol )
What is power set of power set of an empty set?
It is the set comprising the following 4 elements:phi,{phi},{{phi}} and{phi, {phi}}
Is a empty set a proper subset explain with reason?
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.
Is power set of singleton set equal to null set?
No. Let A = {a} (a singleton set) then P(A) = {a, 0} where 0 is the null (empty) set.
Is an empty set a subset of itself?
Yes it is. Everything in the empty set (which is nothing of course) is also in the empty set. If it's not in the empty set, it's not in the empty set. The empty set has no propersubsets, though, or subsets that are different from it.
Is an empty set a subset of every set?
Yes,an empty set is the subset of every set. The subset of an empty set is only an empty set itself.
What is the meaning of empty set?
The empty set is the set that contains no elements. (It is the empty set, not an empty set, because there is only one of them. It is a unique mathematical object.)
What is empty set?
difinition of empty set
What isan empty set?
The empty set is a set that has no elements.
What will be the representation of subset of a empty set?
The only subset of an empty set is the empty set itself.
Is empty set a set and how?
empty set is a set because its name indicate as it is the set.
Why empty set is proper subset of every set?
It isn't. The empty set is a subset - but not a proper subset - of the empty set.
