Misc 2 - Chapter 1 Class 11 Sets - Part 13

Misc 2 - Chapter 1 Class 11 Sets - Part 14

Misc 2 - Chapter 1 Class 11 Sets - Part 15

Misc 2 - Chapter 1 Class 11 Sets - Part 16

 

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Misc 2 (vi) Introduction(Example) In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example . (vi) If A ⊂ B and x ∉ B, then x ∉ A Let A = {1}, Since, A ⊂ B ,all elements of set A i.e. 1 should be an element of set B Hence, taking B = {1,2} Let x = 3, So, x is not in set B i.e. x ∉ B. ∈ - (belongs to) element in set ⊂ - is a subset A ⊂ B if all elements of A are in B We have to show that x ∉ A Since 3 is not in set A, 3 ∉ A ∴ x ∉ A So, given Statement is True Since statement is true, we prove generally We have to show that x ∉ A Since 3 is not in set A, 3 ∉ A ∴ x ∉ A So, given Statement is True Since statement is true, we prove generally Misc 2 In each of the following, determine whether the statement is true or false. If it is true, prove it. If it is false, give an example . (vi) If A ⊂ B and x ∉ B, then x ∉ A Let A ⊂ B and x ∉ B. To show: x ∉ A we prove by contradiction Suppose x ∈ A. ∈ - (belongs to) element in set ⊂ - is a subset A ⊂ B if all elements of A are in B Then, x ∈ B, which is a contradiction as x ∉ B ∴ x ∉ A So, given Statement is True

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Davneet Singh

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo