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Q: Is the empty set an element of every 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.

an empty set does not have any element

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

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.

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".

yes, it is.

Yes,an empty set is the subset of every set. The subset of an empty set is only an empty set itself.

The trivial subsets of a set are those subsets which can be found without knowing the contents of the set. The empty set has one trivial subset: the empty set. Every nonempty set S has two distinct trivial subsets: S and the empty set. Explanation: This is due to the following two facts which follow from the definition of subset: Fact 1: Every set is a subset of itself. Fact 2: The empty set is subset of every set. The definition of subset says that if every element of A is also a member of B then A is a subset of B. If A is the empty set then every element of A (all 0 of them) are members of B trivially. If A = B then A is a subset of B because each element of A is a member of A trivially.

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

Every set contains the empty set. Every set is a subset of itself.

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.)

Yes - because, if something is an object of the null set, then it is also an element of the other set. Since nothing is an element of the empty set, the above statement is trivially true.

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