Since B is a subset of A, all elements of B are in A.
If the elements of B are deleted, then B is an empty set, and also it is a subset of A, moreover B is a proper subset of A.
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Suppose A is a subset of S. Then the complement of subset A in S consists of all elements of S that are not in A. The intersection of two sets A and B consists of all elements that are in A as well as in B.
If all elements of set A are also elements of set B, then set A is a subset of set B.
This problem can be modeled and tested quite easily. Set A can be [X,Y], subset B [X,Y], and subset A [X,Y]. Therefore A and B are equivalent.
For example, if we have a set of numbers called A which has 3 members(in our case numbers): A={2,5,6} this set has 8 subsets (2^3) which are as follow: the empty set: ∅ {2},{5},{6} {2,5},{2,6},{5,6} {2,5,6}
An improper subset is identical to the set of which it is a subset. For example: Set A: {1, 2, 3, 4, 5} Set B: {1, 2, 3, 4, 5} Set B is an improper subset of Set Aand vice versa.