Final answer:
Yes, a complement roster form can be long depending on the size of the universal set and the subset in question within the context of set theory. Complement rosters include all elements not in the subset but present in the universal set, and their length varies accordingly. option (A)
Step-by-step explanation:
Can a complement roster form be long? The answer is A. Yes. The length of a complement roster form depends on the context. In set theory, a 'complement' refers to elements not in the subset but are in the universal set. If the universal set is large and the subset is small, the complement can indeed be very long, containing many elements. Conversely, if the subset is large and the universal set is not much larger, the complement could be short.
For example, if the universal set is all integers from 1 to 1000, and the subset is the numbers 1 to 10, the complement roster would be the numbers 11 to 1000, which is quite long. However, it is important to note that there is no theoretical limit to how long the roster can be, so long as there are more elements outside the subset within the universal set.