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

Misc 5 - Misc 5
Show that if A ⊂ B, then C – B ⊂ C – A.



To show: If A ⊂ B, then C – B ⊂ C – A

Proo - Miscellaneous

  1. Chapter 1 Class 11 Sets
  2. Serial order wise
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Transcript

Misc 5 Show that if A ⊂ B, then C – B ⊂ C – A. Introduction 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 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 ∈ 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 is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
  • yatish paul's image
    What if we have to do the reciprocal like prove:-
    C-A c C-B. Do we have to do like you did till the last where x belongs to C-B and x belongs to   C-A and then say therefore C-A c C-B.

    View answer
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