Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What characterizes a proper subset?

A is equal to B
A is not equal to B
A contains all elements of B
B is not a subset of A

The correct answer is: A is not equal to B

A proper subset is characterized by the relationship between two sets where one set, referred to as the proper subset, contains some—but not all—elements of another set. In this case, when it is stated that set A is not equal to set B, it implies that A has fewer elements than B, establishing that A is a proper subset of B. A proper subset also emphasizes that there must be at least one element in B that is not found in A, thus confirming the distinction and reinforcing the idea of a proper subset. The focus on the inequality between sets strengthens the understanding of subset relationships in set theory. A proper subset cannot contain all elements of the larger set, nor can the two sets be identical; therefore, the absence of equality between them is essential. This helps distinguish proper subsets from non-proper subsets, where the two sets may be equal. Understanding this concept helps educators effectively communicate with students about foundational ideas in set theory and relationships between different sets.