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Let A ={3,6,12,15,18,21} and B- {4,8,12,...

Let A ={3,6,12,15,18,21} and B- {4,8,12,16,20} and C = {2,4,6,8,10,12,14,16} , then :
(i) A-B = ………
(ii) B-C = ……..

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, we will find the differences between the sets A and B, and B and C as specified in the question. ### Given Sets: - \( A = \{3, 6, 12, 15, 18, 21\} \) - \( B = \{4, 8, 12, 16, 20\} \) - \( C = \{2, 4, 6, 8, 10, 12, 14, 16\} \) ### (i) Finding \( A - B \): 1. **Identify elements in A**: The elements in set A are 3, 6, 12, 15, 18, and 21. 2. **Identify elements in B**: The elements in set B are 4, 8, 12, 16, and 20. 3. **Find common elements**: The common element between A and B is 12. 4. **Subtract common elements from A**: Remove 12 from A. - Remaining elements in A after removing 12: \( \{3, 6, 15, 18, 21\} \) Thus, \( A - B = \{3, 6, 15, 18, 21\} \). ### (ii) Finding \( B - C \): 1. **Identify elements in B**: The elements in set B are 4, 8, 12, 16, and 20. 2. **Identify elements in C**: The elements in set C are 2, 4, 6, 8, 10, 12, 14, and 16. 3. **Find common elements**: The common elements between B and C are 4, 8, 12, and 16. 4. **Subtract common elements from B**: Remove 4, 8, 12, and 16 from B. - Remaining element in B after removing these: \( \{20\} \) Thus, \( B - C = \{20\} \). ### Final Answers: - (i) \( A - B = \{3, 6, 15, 18, 21\} \) - (ii) \( B - C = \{20\} \)
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