To solve the problem of finding the intersection $A \cap B$, we need to identify the common elements in sets $A$ and $B$.

Given sets: $A = \{-2, -1, 0, 1, 2\}$ $B = \{2k \mid k \in A\}$

First, we calculate the elements of set $B$:

For each $k \in A$:

• If $k = -2$, then $2k = 2(-2) = -4$
• If $k = -1$, then $2k = 2(-1) = -2$
• If $k = 0$, then $2k = 2(0) = 0$
• If $k = 1$, then $2k = 2(1) = 2$
• If $k = 2$, then $2k = 2(2) = 4$

Thus, the set $B$ is: $B = \{-4, -2, 0, 2, 4\}$

Now, we find the intersection $A \cap B$ by identifying the common elements in both sets $A$ and $B$: $A = \{-2, -1, 0, 1, 2\}$ $B = \{-4, -2, 0, 2, 4\}$

The common elements are: $A \cap B = \{-2, 0, 2\}$

Thus, the correct answer is (D) $\{-2, 0, 2\}$.

Do you want details or have any questions? Here are 5 numbered questions you might find useful:

1. How do you find the union of two sets?
2. What is the difference between intersection and union in set theory?
3. Can you explain how to determine the elements of a set given a condition?
4. How would the intersection change if the sets were different?
5. What are the applications of set intersections in real life?

Tip: When working with sets, always ensure to list out all potential elements carefully before identifying commonalities.