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Misc 5 - Show that if A < B, then C – B < C – A - Chapter 1

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Misc 5 - Chapter 1 Class 11 Sets - Part 2

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Misc 5 - Introduction Show that if A ⊂ B, then C – B ⊂ C – A. Let A = {1, 2} , B = {1, 2, 3}, C = {1, 2, 3, 4} C – B = {1, 2, 3, 4} – {1, 2, 3} = {4} C – A = {1, 2, 3, 4} – {1, 2} = {3, 4} {4} ⊂ {3, 4} So, C – B ⊂ C – A ⊂ - is a subset A ⊂ B if all elements of A are in B Misc 5 Show that if A ⊂ B, then C – B ⊂ C – A. To show: If A ⊂ B, then C – B ⊂ C – A Proof: Let x be in an element of set C – B i.e. x ∈ C – B ⇒ So, x is in set C, but not in set B , i.e. x ∈ C and x ∉ B ⇒ x is in set C, but not in set A i.e. x ∈ C and x ∉ A ⇒ So, x is in set C – A i.e. x ∈ C – A If x is not in set B, x is not set A as A is a subset of B ⊂ - is a subset A ⊂ B if all elements of A are in B ∈ Belongs to – Element of set ∴ If x ∈ C – B ,then x ∈ C – A i.e. If an element belongs to the set C – B , it also belongs to the set C – A ⇒ C – B ⊂ C – A Hence proved

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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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.