(3) Let $A \subseteq \mathbb{R}$ be nonempty and bounded above. Define
\[
-A:=\{-x \mid x \in A\} .
\]
Answer
Let $A \subseteq \mathbb{R}$ be nonempty and bounded above. Define $-A:=\{-x \mid x \in A\}$ . This is the set of all negative values of elements in set A. This function takes a set A as input and returns a new set where each element is the negative of the corresponding element in A. The final answer is the function itself, which defines the set -A as required. The function is: \(\boxed{\text{def negative_set(A): return \{-x for x in A\}}}\)
Step 1 ：Let $A \subseteq \mathbb{R}$ be nonempty and bounded above. Define $-A:=\{-x \mid x \in A\}$ . This is the set of all negative values of elements in set A. This function takes a set A as input and returns a new set where each element is the negative of the corresponding element in A. The final answer is the function itself, which defines the set -A as required. The function is: \(\boxed{\text{def negative_set(A): return \{-x for x in A\}}}\)
