If "aο ∩ b = b," what relationship is being expressed?

The expression "aο ∩ b = b" indicates that the intersection of sets a and b results in set b itself. This means that all elements (or points) in set b are also contained within set a. In other words, every point that exists in set b is also found in set a.

This establishes a relationship where set b is entirely contained within set a, which is why the correct interpretation is that every point of set b is a point of set a. A situation like this illustrates the concept of subset relationships in set theory, reinforcing that b is fully encompassed by a.

On the other hand, if one were to interpret the other choices, they would reflect different relationships. For example, stating that every point of a is a point of b would imply set a is a subset of set b, which contradicts the given intersection relationship. Describing the sets as disjoint would suggest that there are no points in common between them, which is also contrary to the stated relationship. Similarly, claiming they touch at multiple points does not adequately reflect the nature of the intersection being equal to b; this would imply that both sets have some shared elements but does not clarify the complete containment expressed in the original statement.