The problem you've provided is a set theory problem involving the following sets:

• U (the universal set) = {1, 2, 3, 4, 5, 6, 7, 8, 9}
• A (odd numbers less than 10) = {1, 3, 5, 7, 9}
• B = {2, 4, 5, 6, 8}
• C = {3, 6, 7, 9}

Questions

The questions involve operations like union ( ∪ ), intersection ( ∩ ), difference ( − ), and complement (denoted by superscript c, e.g., $A^c$).

Let's break down some of these questions and calculate the answers.

a. $A - B$

This means the elements in $A$ that are not in $B$.

• $A$ = {1, 3, 5, 7, 9}
• $B$ = {2, 4, 5, 6, 8}

So, $A - B$ = {1, 3, 7, 9} (remove 5 since it's in $B$).

b. $A \cap B$

This means the intersection of sets $A$ and $B$, which are the common elements between $A$ and $B$.

• $A \cap B$ = {5} (the only common element).

c. $A^c$

This is the complement of $A$ with respect to the universal set $U$. It contains elements in $U$ that are not in $A$.

• $U$ = {1, 2, 3, 4, 5, 6, 7, 8, 9}
• $A$ = {1, 3, 5, 7, 9}

Thus, $A^c$ = {2, 4, 6, 8} (all even numbers).

d. $A \cap B^c$

This means the intersection of $A$ with the complement of $B$ (elements in $U$ but not in $B$).

• $B^c$ = {1, 3, 7, 9} (elements in $U$ but not in $B$)
• $A$ = {1, 3, 5, 7, 9}

Thus, $A \cap B^c$ = {1, 3, 7, 9}.

Would you like me to continue with the remaining operations or provide any clarifications?

Related questions:

1. What is the result of $B - A$?
2. Can you calculate $B^c \cap C$?
3. How do we calculate $A \cup B$?
4. What is the result of $A \cap C$?
5. What is $(A \cap B) \cup (A \cap C)$?

Tip:

For set complements, always remember that $A^c = U - A$, meaning all elements in the universal set $U$ that are not in $A$.