An empty set is a subset of any set, and a non-empty proper subset is a subset except the empty set and the original set.

Non-empty proper subset is proper subset of B, but A is not an empty set, so A is a non-empty proper subset of B. If there are n elements in B, then B has 2 n subsets and a non-empty proper subset (2 n)-2.

Extended data:

If set A is a subset of set B and set B is not a subset of set A, then set A is called the proper subset of set B. If A is contained in B and A is not equal to B, then set A is called the proper subset of set B. ..

proper subset

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.

Non-empty proper subset: If a is set? B, and set A≦? , set a is the nonempty proper subset of set b.

If A is proper subset of B (that is, A? B and A≠B), and A≦? Let A be a nonempty proper subset of B. If there are n elements in A, A has 2 n subsets, (2 n- 1) proper subset and (2 n-2) nonempty proper subset.

Set is a basic concept in mathematics. Explain first. For example, the books in the bookcase form a set, the students in the classroom form a set, and all the real numbers form a set. Generally speaking, the so-called set (referred to as "set") refers to the sum of things with certain properties, and the things that make up this set are called elements of the set (referred to as "elements"). Collections are usually represented by uppercase letters, and elements are represented by lowercase letters. For example, a∈A, that is, element A belongs to set A.

References:

Baidu Encyclopedia-Non-empty proper subset? Baidu Encyclopedia-proper subset