are these two sets equal, equivalent, both, or neither?
A = the set of U.S. states
B = the set of U.S. state capitals
Neither.
The sets A and B are related, but they are neither equal nor equivalent.
Set A, the set of U.S. states, includes all 50 states such as California, New York, Texas, etc.
Set B, the set of U.S. state capitals, includes the capital cities of each state such as Sacramento (capital of California), Albany (capital of New York), Austin (capital of Texas), etc.
While each state has a corresponding capital city, the sets A and B have different elements. Therefore, they are not equal. Additionally, the sets A and B do not have the same cardinality, meaning they do not have the same number of elements. Hence, they are not equivalent either.