Class 11  Chapter -1 Set Theory Miscellaneous Exercise NCERT solution of chapter 1, class 11, miscellaneous exercise, Union of sets, intersection of sets, complement of sets and Venn diagram of sets, word problems on sets. Q1) A = {x : x ∈ R and x satisfy x 2 -8x+12 = 0} B = {2, 4, 6},  C = {2, 4, 6, 8, ....}, D = {6} Solution: x 2  - 8x + 12 = 0 ⇒ x 2  - 6x - 2x + 12 = 0 ⇒ x(x - 6) -2(x - 6) = 0 ⇒ (x - 2)(x - 6) = 0 ⇒ x = 2, x = 6 ⇒ A = {2, 6} A ⊂ B,  A ⊂ C, B ⊂ C, D ⊂ A,  D ⊂ B,  D ⊂ C Q2) (i) If x ∈ A and A∈B, then x ∈ B Ans:  False Statement Reason: If A = {1,2}, B={{1,2}, 3} Here 1∈A and A ∈ B but 1 ∉ B So given statement is false (ii) If A ⊂ B and B ∈ C, then A ∈ C Let A = {1}, B={1, 2}, C ={{1, 2}, 3} Here  A ⊂ B  and B ∈ C,  But 1∉ C So this is a false statement (iii) If A ⊂ B and B ⊂ C, then A ⊂ C Ans: True Statement Explanation:  Let A={1}, B={1,2}, C = {1,2,3} Here  1 ∈ A and 1 ∈ B  ⇒ A  ⊂ B .... (1) 1, 2 ∈ B and 1,2 ∈ C  ⇒ B  ⊂ C ....... (2) From (1) and (2) we get  A ⊂ C

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COMMON ERRORS DONE BY STUDENTS   Class 12, Mathematics:  Common errors or common mistakes done by students while solving the questions in the examination, Common mistakes done by the students of class XII while solving the mathematical problems. Chapter 1 Relations and Functions