Let's find each of these set operations:

1. $A - B$ (Elements in $A$ but not in $B$):

• $A = \{12, 15, 17, 20, 21\}$
• $B = \{12, 14, 16, 18, 21\}$

Finding elements in $A$ but not in $B$: $A - B = \{15, 17, 20\}$

2. $B - C$ (Elements in $B$ but not in $C$):

• $B = \{12, 14, 16, 18, 21\}$
• $C = \{15, 17, 18, 22\}$

Finding elements in $B$ but not in $C$: $B - C = \{12, 14, 16, 21\}$

3. $C - A$ (Elements in $C$ but not in $A$):

• $C = \{15, 17, 18, 22\}$
• $A = \{12, 15, 17, 20, 21\}$

Finding elements in $C$ but not in $A$: $C - A = \{18, 22\}$

4. $B - A$ (Elements in $B$ but not in $A$):

• $B = \{12, 14, 16, 18, 21\}$
• $A = \{12, 15, 17, 20, 21\}$

Finding elements in $B$ but not in $A$: $B - A = \{14, 16, 18\}$

5. $A - A$ (Elements in $A$ but not in $A$):

Since this represents the difference of a set with itself, it will always be the empty set: $A - A = \emptyset$

Final Answers:

1. $A - B = \{15, 17, 20\}$
2. $B - C = \{12, 14, 16, 21\}$
3. $C - A = \{18, 22\}$
4. $B - A = \{14, 16, 18\}$
5. $A - A = \emptyset$

Would you like more details on these solutions or have any questions?

Relative Questions:

1. What is the union of sets $A$ and $B$?
2. What is the intersection of sets $B$ and $C$?
3. What would $C - B$ be in this context?
4. How would the complement of set $A$ in the universal set look?
5. Can two different sets have an empty difference?

Tip:

When subtracting sets ($X - Y$), list the elements in $X$ that are not in $Y$, ensuring no overlap with $Y$'s elements.