CBSE Mathematics

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 Let A = { 1, 2, 3}. Check whether R = { (1, 2), (2, 1), (1, 1), (1, 3)} is symmetric or not. Common Error : Here, (1, 2) ∈ R , (2,1) ∈ R. So, it is symmetric. Correction : The student thinks that only an ordered pair is to check for Symmetric. So, he forgets to check for (1, 3). If A = {1, 2, 3}, check whether R = {(1, 1), (1, 2), (2, 1)} is transitive or not. Common Error : (1,2) ∈ R , (2,1) ∈ R ⇒ that (1,1) ∈ R. So it is transitive.  Correction : Here the student forgets to see for (2, 1) ∈ R , (1, 2) ∈ R implies (2, 2) ∈ R or not Show that relation R in the set A ={1, 2, 3, 4, 5 } given by R = {(a, b) : |a - b| is even }, is an equivalence relation. Common Error : Student forget to write ± while proving tran