Last updated at May 29, 2018 by Teachoo

Transcript

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) 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) B = B (A X) Using distributive law :A (B C)= (A B) (A C) = (B A) (B X) As B X = = (B A) B = B A B = A B From (1) and (2), A = A B & B = A B A = B Hence proved

Proof - Using properties of sets

Chapter 1 Class 11 Sets

Concept wise

- Depiction and Defination
- Depicition of sets - Roster form
- Depicition of sets - Set builder form
- Intervals
- Null Set
- Finite/Infinite
- Equal sets
- Subset
- Power Set
- Universal Set
- Venn Diagram and Union of Set
- Intersection of Sets
- Difference of sets
- Complement of set
- Number of elements in set - 2 sets (Direct)
- Number of elements in set - 2 sets - (Using properties)
- Number of elements in set - 3 sets
- Proof - Using properties of sets
- Proof - where properties of sets cant be applied,using element

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.