If A⊂B, then which one of the following is true?
When we say that A is a subset of B, it means that every element of set A is also an element of set B. In other words, A is contained within B. Based on this definition, the following statement is true:
- B contains at least one element that A does not contain
If A is a subset of B, it means that all the elements in A are also in B. Therefore, there cannot be any element in B that is not in A. This makes option A incorrect.
Option B is also incorrect because it suggests that A and B are equal sets. However, if A is a proper subset of B, then there must be at least one element in B that is not in A.
Option C is incorrect because it suggests that A and B have no elements in common. However, since A is a subset of B, all the elements in A are also in B. Therefore, A and B must have at least one element in common.
Option D is correct because A being a proper subset of B means that there is at least one element in B that is not in A. Therefore, option D is the correct answer.