To find the union of the sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex], we combine all the elements from both sets without any repetition. Here are the steps to determine [tex]\(A \cup B\)[/tex]:
1. List all elements in set [tex]\(A\)[/tex]: [tex]\(\{2, 10, 18, 25\}\)[/tex].
2. List all elements in set [tex]\(B\)[/tex]: [tex]\(\{6, 13, 22, 2, 32, 25\}\)[/tex].
Next, we combine these elements, ensuring that each element appears only once in the resulting set:
3. Start with all elements in [tex]\(A\)[/tex]:
[tex]\(\{2, 10, 18, 25\}\)[/tex].
4. Add elements from [tex]\(B\)[/tex] that are not already in [tex]\(A\)[/tex]:
- [tex]\(6\)[/tex] is not in [tex]\(A\)[/tex], so add [tex]\(6\)[/tex].
- [tex]\(13\)[/tex] is not in [tex]\(A\)[/tex], so add [tex]\(13\)[/tex].
- [tex]\(22\)[/tex] is not in [tex]\(A\)[/tex], so add [tex]\(22\)[/tex].
- [tex]\(2\)[/tex] is already in [tex]\(A\)[/tex], so do not add [tex]\(2\)[/tex].
- [tex]\(32\)[/tex] is not in [tex]\(A\)[/tex], so add [tex]\(32\)[/tex].
- [tex]\(25\)[/tex] is already in [tex]\(A\)[/tex], so do not add [tex]\(25\)[/tex].
Combining all unique elements gives us: [tex]\(\{2, 6, 10, 13, 18, 22, 25, 32\}\)[/tex].
Therefore, the union of sets [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is [tex]\(\{2, 6, 10, 13, 18, 22, 25, 32\}\)[/tex].
Thus, the correct answer is:
c. [tex]\(\{2, 6, 10, 13, 18, 22, 25, 32\}\)[/tex]
