Final answer:
The student is asked to determine the truth value of statements related to a set A and other mathematical concepts.
Step-by-step explanation:
The question requires determining the truth value of statements given a set a = {4, 5, 7, 8, 9}. For example, the statement f. A' consists of all outcomes in the sample space, S, that DO NOT lie in A, so A' = 1, 3, 5, 7, 9, 11, 13, 15, 17, 10, would need to be evaluated. If we consider the universal set U as the set of natural numbers, then A' would indeed be the set of natural numbers not in set A. However, this provided A' includes some numbers such as 5, 7, and 9 that are indeed in A so the statement is false. The correct A' should exclude those elements and only include natural numbers that are not in A.
The task also involves simplifying algebraic expressions and optimizing solutions for reasonableness. It requires understanding not just the mechanical process of simplifying expressions but also verifying the rationale behind the steps taken.
In summary, each statement must be scrutinized in the context of the provided set A as well as mathematical concepts such as simplification of algebra and the evaluation of the reasonableness of the solutions.