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Question 1 - Proof - where properties of sets cant be applied,using element - Chapter 1 Class 11 Sets
Last updated at April 16, 2024 by Teachoo
Proof - where properties of sets cant be applied,using element
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
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Proof - where properties of sets cant be applied,using element
Transcript
Question 1 Assume that P (A) = P (B). Show that A = B. In order to prove A = B, we should prove A is a subset of B i.e. A ⊂ B & B is a subset of A i.e. B ⊂ A Set A is an element of power set of A as every set is a subset (Eg: for set A = {0, 1} , P(A) = { ∅ , {0}, {1}, {0, 1} } So, A is in P(A)) i.e. A ∈ P(A) ⇒ A ∈ P(B) If set A is in power set of B, set A is a subset of B ∴ A ⊂ B ⊂ Subset A ⊂ B (All elements of set A in set B) Similarly, We can prove B ⊂ A Now since A ⊂ B & B ⊂ A ∴ A = B Hence proved
