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
