If A={12,15,17,20,21}B={12,14,16,18,21} and C={15,17,18,22}then find A-B, B- C, C-A,
B-A, A-A

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.

If A={12,15,17,20,21} B={12,14,16,18,21} and C={15,17,18,22} then find A-B, B-C, C-A, B-A, A-A

Learn how to find the set differences A - B, B - C, C - A, B - A, and A - A for sets A={12,15,17,20,21}, B={12,14,16,18,21}, and C={15,17,18,22}. This solution covers core set theory concepts and the properties of set difference operations. Suitable for students in Grades 9-10.

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