Last updated at Sept. 3, 2021 by Teachoo

Transcript

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

Miscellaneous

Misc 1

Misc 2 (i)

Misc 2 (ii) Important

Misc 2 (iii) Important

Misc 2 (iv)

Misc 2 (v)

Misc 2 (vi) Important

Misc 3

Misc 4 Important

Misc 5 You are here

Misc 6

Misc 7 Important

Misc 8 Important

Misc 9 Important

Misc 10

Misc 11

Misc 12 Important

Misc 13 Important

Misc 14

Misc 15 Important

Misc 16 Important

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.