The Venn diagram you've shared contains two sets, $A$ and $B$, within the universal set $S$. To answer the question, we need to find the elements of the following sets:

1. Set $S$ (the universal set)
2. Set $A$ (the elements in circle $A$)
3. Set $B$ (the elements in circle $B$)
4. $A \cap B$ (the intersection of $A$ and $B$, i.e., elements common to both)
5. $A^c$ (the complement of $A$, i.e., elements in $S$ but not in $A$)
6. $B^c$ (the complement of $B$, i.e., elements in $S$ but not in $B$)

From the diagram:

• Set $A$ contains: $\{1, 3, 4, 6, 10\}$
• Set $B$ contains: $\{4, 5, 6, 11, 12, 13, 14\}$
• The universal set $S$ includes all the numbers in the diagram: $\{1, 3, 4, 5, 6, 10, 11, 12, 13, 14, 7, 8, 9, 15\}$
• The intersection $A \cap B$ (common elements between $A$ and $B$): $\{4, 6\}$
• The complement of $A$, $A^c$, is: $\{5, 7, 8, 9, 11, 12, 13, 14, 15\}$ (elements in $S$ that are not in $A$)
• The complement of $B$, $B^c$, is: $\{1, 3, 7, 8, 9, 10, 15\}$ (elements in $S$ that are not in $B$)

Would you like a deeper explanation on any of these sets? Here are 5 related questions for further practice:

1. How would you find the union of sets $A$ and $B$?
2. What is the difference between $A \setminus B$ and $B \setminus A$?
3. Can you list the elements of $A \cup B$ (union of $A$ and $B$)?
4. How would the Venn diagram change if we added a new element only to $A \cap B$?
5. What is the set $(A \cup B)^c$?

Tip: To easily understand complements, always think of it as “everything outside the set” in relation to the universal set.