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Yes, the empty set is a subset of any set.
Recall the definition: A is a subset of B if every element in A is also in B. But A is empty so one can assign any property (including "membership in B") to its elements and the property will hold.
Statement "every seven-legged alligator is orange" is true for the same reason.
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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.
What is the subset of 5564?
The only subsets of the set containing 5564 is the empty set and the set {5564}.
What is subset of set?
Given a set, S, a subset A of S is set containing none or more elements of S. So by definition, the subset A is a set.If there exists some element that is in S but not in A then A is a pro[er subset of S.
Difference between subset and proper subset?
A subset of a set S can be S itself. A proper subset cannot.
What the example of improper subset?
If you have a set S, the only improper subset of S is S itself. An improper subset contains all elements of S and no others. It is therefore equivalent to S. For example if S ={1,2,3} then the improper subset is {1,2,3}, and an example proper subset is {1,2}.
