Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class

Miscellaneous

Misc 1

Misc 2 (i)

Misc 2 (ii) Important

Misc 2 (iii) Important

Misc 2 (iv)

Misc 2 (v)

Misc 2 (vi) Important

Misc 3

Misc 4 Important

Misc 5

Misc 6 Important

Misc 7 Important

Misc 8 You are here

Misc 9

Misc 10 Important

Question 1 Deleted for CBSE Board 2024 Exams

Question 2 Important Deleted for CBSE Board 2024 Exams

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Question 4 Deleted for CBSE Board 2024 Exams

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Question 6 Important Deleted for CBSE Board 2024 Exams

Chapter 1 Class 11 Sets

Serial order wise

Last updated at May 29, 2023 by Teachoo

Misc 8 Show that A ∩ B = A ∩ C need not imply B = C. We have to prove false, so we take a example It is given that A ∩ B = A ∩ C i.e. Common element in set A & B = Common element in set A & C Let A = {0, 1}, B = {0, 2, 3}, and C = {0, 4, 5} A ∩ B = {0} and A ∩ C = {0} Here, A ∩ B = A ∩ C = {0} But B ≠ C as 2 is in set B, but not in A Hence proved Misc 11 Let A and B be sets. If A ∩ X = B ∩ X = ∅ and A ∪ X = B ∪ X for some set X, show that A = B. (Hints: A = A ∩ (A ∪ X), B = B ∩ (B ∪ X) and use distributive law) Given: Let A and B be two sets such that A ∩ X = B ∩ X = ∅ and A ∪ X = B ∪ X for some set X. To prove: A = B Proof: Let A = A ∩ (A ∪ X) A = A ∩ (B ∪ X) (Given A ∪ X = B ∪ X) Let A = A ∩ (A ∪ X) Given A ∪ X = B ∪ X A = A ∩ (B ∪ X) Using distributive law : A ∩ (B ∪ C)= (A ∩ B) ∪ (A ∩ C) = (A ∩ B) ∪ (A ∩ X) As A ∩ X = ∅ given = (A ∩ B) ∪ ∅ A = A ∩ B Let B = B ∩ (B ∪ X) Given A ∪ X = B ∪ X B = B ∩ (A ∪ X) Using distributive law: A ∪ (B ∩ C)= (A ∩ B) ∪ (A ∩ C) = (B ∩ A) ∪ (B ∩ X) As B ∩ X = Φ = (B ∩ A) ∪ Φ B = B ∩ A B = A ∩ B From (1) and (2), A = A ∩ B & B = A ∩ B ∴ A = B Hence proved