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Q: When is an empty set an element of a set?

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The empty element is a subset of any set--the empty set is even a subset of itself. But it is not an element of every set; in particular, the empty set cannot be an element of itself because the empty set has no elements.

yes, it is.

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.

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.)

empty set is a set because its name indicate as it is the set.

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The empty element is a subset of any set--the empty set is even a subset of itself. But it is not an element of every set; in particular, the empty set cannot be an element of itself because the empty set has no elements.

No. An empty set is a subset of every set but it is not an element of every set.

yes, it is.

empty set or null set is a set with no element.

I believe you are talking about subsets. The empty set (set with no elements) is a subset of any set, including of the empty set. ("If an object is an element of set A, then it is also an element of set B." Since no element is an element of set A, the statement is vacuously true.)

Any set has the empty set as subset A is a subset of B if each element of A is an element of B For the empty set ∅ the vacuum property holds For every element of ∅ whatever property holds, also being element of an arbitrary set B, therefore ∅ is a subset of any set, even itself ∅ has an unique subset: itself

A relation R is a set A is called empty relation if no element of A is related to any element of R

Because every member of the empty set (no such thing) is a member of any given set. Alternatively, there is no element in the empty set that is missing from the given set.

No. Zero is a number, so the "set of zero" contains one element. The empty set, also known as the null set, contains no elements.

Because every member of the empty set is also a member of the other set. "If x is an element of the empty set, then it is also an element of the other set." Because the first part of the "if" is always false, the result is true. If this doesn't seem logical, see the Wikipedia article on "Vacuous truth".

No, an empty set can't be the super set.The definition of super set is as follows:If A and B are sets, and every element of A is also an element of B, then B is the super set of A, denoted by B ⊇ A.Another way to interpret this is A ⊆ B, which means that "A is the subset of B".Suppose that ∅ is the super set. This implies:∅ ⊇ A [Which is not true! Contradiction!]Remember that ∅ and {∅} are two different sets. If we have {∅}, then there exists an element that belongs to that set since ∅ is contained in that set. On the other hand, ∅ doesn't have any element, including ∅.Therefore, an empty set can't be the super 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.An empty set is not a proper subset of an empty set.

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