First, subset definition:

Generally speaking, for two sets A and B, if any element in set A is an element in set B, we say that these two sets have an inclusion relationship, and call set A a subset of set B ... and call it a? B (or b? A), pronounced "A is contained in B" (or "B contains A").

That is to say, for sets a and b,? X∈A has x∈B, so what about A? B. As we all know, any set A is a subset of itself, and an empty set is a subset of any set.

Second, proper subset definition:

If you set one? B, there is an element x∈B, and the element X does not belong to the set A. We say that the set A and the set B have a true inclusion relationship, and the set A is the proper subset of the set B, which is denoted as A? B (or b? A), pronounced "A really contains B" (or "B really contains A").

That is to say, for sets a and b,? X∈A has x∈B, and? X∈B and x A, then a? B an empty set is a proper subset of any non-empty set.

Third, proper subset is not empty.

If you set one? B, and set A≦? , set a is the nonempty proper subset of set b.

The nature of the set:

1, empty set is unique:

An empty set is a collection without any elements. All collections contain empty sets. An empty set is unique, that is, there are no two different empty sets.

2, the definition of subset:

If all the elements in set A belong to set B, then set A is a subset of set B. Set A is a subset of set B, and set B is denoted as a? B if set a is not a subset of set b, then it is recorded as a? B.

3, the definition of trade unions:

The union of set a and set b is a set containing all elements in a and b, and it is denoted as a ∪ b. If an element belongs to set A or set B, it must belong to set A ∪ B. ..

4, the definition of intersection:

The intersection of set a and set b is a set containing the same elements in a and b, and it is marked as a ∩ b. If an element belongs to both set A and set B, it must belong to set A ∩ B. ..

5, the definition of complement set:

The complement of the set A in the set B refers to the set composed of elements belonging to B but not to A, and is recorded as B \ A. ..