Final answer:
The set C is distinct from sets A and B and has no common elements with them. To determine (A ∪ B)C, we first find the union of A and B within the universal set and then find the complement of this union, which results in the set {21, 25, 27, 33}.
Step-by-step explanation:
The student's question involves understanding sets, set operations, and related concepts. The universal set in question is composed of whole numbers between 20 and 35. Set A consists of even numbers and set B consists of prime numbers. The set C = {21, 25, 27, 33} does not contain any even numbers, so it does not intersect with set A. It also does not include any prime numbers; therefore, it has no common elements with set B.
The elements of A within the universal set would be {22, 24, 26, 28, 30, 32, 34}, and the elements of B would include any primes within the given range, which are {23, 29, 31}. Thus, the union (A ∪ B) within the universal set includes all elements that are either even or prime, which would be {22, 23, 24, 26, 28, 29, 30, 31, 32, 34}. The complement of this set (all elements in the universal set not in the union) would therefore include {21, 25, 27, 33, 35}. Since 35 is not in the universal set defined by the question, the final answer for (A ∪ B)C is {21, 25, 27, 33}.