What does "a ∩ b = a" imply about the relationship between a and b?

The expression "a ∩ b = a" indicates that the intersection of sets a and b results in set a. This means that all elements of set a are also contained within set b. In other words, every item that exists in set a can also be found in set b, which defines the relationship where set a is a subset of set b.

This relationship is typical in set theory, where the intersection of a set with any set that contains it will always yield the original set. Thus, in this case, the implication is that set a is entirely within the boundaries of set b, confirming that all the elements of set a exist within set b.

Other interpretations, like whether the sets are equal or disjoint, do not hold true under this scenario, as this equality signifies inclusion rather than complete equality or a lack of common elements.