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Misc 1 - Which sets are subsets A = {x: x satisfy x2 - 8x + 12 - Miscellaneous

  1. Chapter 1 Class 11 Sets
  2. Serial order wise
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Misc 1 Decide, among the following sets, which sets are subsets of one and another: A = {x: x ∈ R and x satisfy x2 – 8x + 12 = 0}, B = {2, 4, 6}, C = {2, 4, 6, 8…}, D = {6}. A = {x: x ∈ R and x satisfies x2 – 8x + 12 = 0} Solving x2 – 8x + 12 = 0 x2 – 6x -2x + 12 = 0 x (x– 6) -2(x – 6) = 0 x = 2, 6 ∴ A = {2, 6} Thus, A = {2, 6}, B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6} A = {2, 6}, B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6} A Since all elements of A are in B, A is a subset of B, i.e. A ⊂ B Since all elements of A are in C , A is a subset of C. , i.e. A ⊂ C B Since all elements of B are in C, B is a subset of C, i.e. B ⊂ C C C is not a subset of any set. A = {2, 6}, B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6} D Since all elements of D is in A, D is a subset of A , i.e. D ⊂ A Since all elements of D are in B, D is a subset of B, i.e. D ⊂ B Since all elements of D are in C, D is a subset of C, i.e. D ⊂ C

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Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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