Let $S$ be the universal set, where:
\[
S=\{1,2,3, \ldots, 28,29,30\}
\]
Let sets $A$ and $B$ be subsets of $S$, where:
Set $A=\{1,2,4,6,9,12,16,23,24,29\}$
Set $B=\{2,5,10,12\}$
Set $C=\{1,11,12,15,17,18,22,28,30\}$
LIST the elements in the set $(A \cup B \cup C)$
\[
(A \cup B \cup C)=\{
\]
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE LIST the elements in the set $(A \cap B \cap C)$
\[
(A \cap B \cap C)=\{
\]
Enter the elements as a list, separated by commas. If the result is the empty set, enter DNE You may want to draw a Venn Diagram to help answer this question.
Answer
So, \(A \cap B \cap C=\boxed{\{12\}}\)
Step 1 ：Define the sets A, B, and C as follows: \(A=\{1,2,4,6,9,12,16,23,24,29\}\), \(B=\{2,5,10,12\}\), and \(C=\{1,11,12,15,17,18,22,28,30\}\)
Step 2 ：To find the union of sets A, B, and C, denoted as \(A \cup B \cup C\), list all the elements in sets A, B, and C, without repeating any elements
Step 3 ：So, \(A \cup B \cup C=\{1,2,4,6,9,12,16,23,24,29,5,10,11,15,17,18,22,28,30\}\)
Step 4 ：To find the intersection of sets A, B, and C, denoted as \(A \cap B \cap C\), list all the elements that are common to sets A, B, and C
Step 5 ：Looking at sets A, B, and C, the only common element is 12
Step 6 ：So, \(A \cap B \cap C=\boxed{\{12\}}\)
