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Last updated at Jan. 27, 2020 by Teachoo

Transcript

Misc 1 Decide, among the following sets, which sets are subsets of one and another: A = {x: x ∈ R and x satisfy x2 – 8x + 12 = 0}, B = {2, 4, 6}, C = {2, 4, 6, 8…}, D = {6}. A = {x: x ∈ R and x satisfies x2 – 8x + 12 = 0} Solving x2 – 8x + 12 = 0 x2 – 6x -2x + 12 = 0 x (x– 6) -2(x – 6) = 0 x = 2, 6 ∴ A = {2, 6} Thus, A = {2, 6}, B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6} A = {2, 6}, B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6} A Since all elements of A are in B, A is a subset of B, i.e. A ⊂ B Since all elements of A are in C , A is a subset of C. , i.e. A ⊂ C B Since all elements of B are in C, B is a subset of C, i.e. B ⊂ C ⊂ - is a subset A ⊂ B if all elements of A are in B A = {2, 6}, B = {2, 4, 6}, C = {2, 4, 6, 8 …}, D = {6} C C is not a subset of any set. D Since all elements of D is in A, D is a subset of A , i.e. D ⊂ A Since all elements of D are in B, D is a subset of B, i.e. D ⊂ B Since all elements of D are in C, D is a subset of C, i.e. D ⊂ C

Chapter 1 Class 11 Sets

Concept wise

- Depiction and Definition
- 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.