Last updated at Dec. 8, 2016 by Teachoo

Transcript

Misc 12, Find sets A, B and C such that A ∩ B, B ∩ C and A ∩ C are non-empty sets and A ∩ B ∩ C = ∅. A ∩ B should be non-empty, i.e. there should be some common element between A & B Similarly, B ∩ C should be non-empty, i.e. there should be some common element between B & C A ∩ C should be non-empty, i.e. there should be some common element between A & C Also, given that A ∩ B ∩ C is a null set, i.e. there should be not be any element common between A, B & C Let A = {0, 1}, B = {1, 2}, and C = {2, 0}. Now, A ∩ B = {1}, B ∩ C = {2}, and A ∩ C = {0}. ∴ A ∩ B, B ∩ C, and A ∩ C are non-empty. However, A ∩ B ∩ C = ∅

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.