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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".
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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.
Is a set containing empty set a subset of itself?
Every set contains the empty set. Every set is a subset of itself.
Is the empty set an element of every set?
No. An empty set is a subset of every set but it is not an element of every set.
What is trivial subset?
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.
Why every set has an empty set?
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
