Question:
Decide, among the following sets, which sets are subsets of one and another:
A = {x: x \(\in\) R and x satisfy \( x^2 - 8x + 12 = 0\)},
B = {2, 4, 6}, C = {2, 4, 6, 8…}, D = {6}.
Decide, among the following sets, which sets are subsets of one and another:
A = {x: x \(\in\) R and x satisfy \( x^2 - 8x + 12 = 0\)},
B = {2, 4, 6}, C = {2, 4, 6, 8…}, D = {6}.
A = {x: x \(\in\) R and x satisfy \( x^2 - 8x + 12 = 0\)},
B = {2, 4, 6}, C = {2, 4, 6, 8…}, D = {6}.
Updated On: Jan 21, 2026
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Solution and Explanation
A = {x: x R and x satisfies \(x^2- 8x + 12 = 0\)}
2 and 6 are the only solutions of \(x^2- 8x + 12 = 0.\)
∴ A = {2, 6}
B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6}
\(∴ D ⊂ A ⊂ B ⊂ C\)
Hence, \(A ⊂ B, A ⊂ C, B ⊂ C, D ⊂ A, D ⊂ B, D ⊂ C\)
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Concepts Used:
Operations on Sets
Some important operations on sets include union, intersection, difference, and the complement of a set, a brief explanation of operations on sets is as follows:
1. Union of Sets:
- The union of sets lists the elements in set A and set B or the elements in both set A and set B.
- For example, {3,4} ∪ {1, 4} = {1, 3, 4}
- It is denoted as “A U B”
2. Intersection of Sets:
- Intersection of sets lists the common elements in set A and B.
- For example, {3,4} ∪ {1, 4} = {4}
- It is denoted as “A ∩ B”
3.Set Difference:
- Set difference is the list of elements in set A which is not present in set B
- For example, {3,4} - {1, 4} = {3}
- It is denoted as “A - B”
4.Set Complement:
- The set complement is the list of all elements present in the Universal set except the elements present in set A
- It is denoted as “U-A”