Final answer:
In the question, sets A and B are subsets of the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Set A includes even numbers less than 20 that are also in U, which are {2, 4, 6, 8, 10}. Set B, in the context of the universal set U, should be an empty set because numbers 14 to 19 are not within U.
Step-by-step explanation:
To provide an answer to the student's question about sets in roster notation, we need to clarify the components of sets A and B within the universal set U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}.
According to provided information, set A consists of even numbers less than 20 that are also in set U, and set B includes numbers from 14 to 19. Therefore, we can define sets A = {2, 4, 6, 8, 10} and B = {}.
However, the roster for set B provided is incomplete in the reference material as the universal set U does not contain numbers larger than 10. Therefore, B should include only numbers that are within the universal set, which in this case, there are none.
Thus set B is an empty set when considering the universal set U provided.
The term "roster notation" refers to listing all elements of a set within curly braces. For example, as per the given details, set A in roster notation is {2, 4, 6, 8, 10}. Set B in roster notation, given the universal set U, should be {}.
Additionally, it's important to note that the reference to A' indicates the complement of A, which contains elements in U that are not in A. Depending on the universal set U, the complement of A could be A' = {1, 3, 5, 7, 9}.