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Misc 1Misc 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} For set 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 For set B Since all elements of B are in C, B is a subset of C, i.e. B ⊂ C A = {2, 6}, B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6} For set C C is not a subset of any set. For set 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 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 ⊂ - is a subset A ⊂ B if all elements of A are in B A = {2, 6}, B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6} C C is not a subset of any set. 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

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.