Misc 2 - Chapter 1 Class 11 Sets - Part 5

Misc 2 - Chapter 1 Class 11 Sets - Part 6

Misc 2 - Chapter 1 Class 11 Sets - Part 7

Misc 2 - Chapter 1 Class 11 Sets - Part 8

Go Ad-free

Transcript

Misc 2 (iii) 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 . (iii) If A ⊂ B and B ⊂ C, then A ⊂ C 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} Also, B ⊂ C, all elements of set B i.e. 1,2 should be an element of set C Hence, taking C = {1,2,3} ∈ - (belongs to) element in set ⊂ - is a subset A ⊂ B if all elements of A are in B We have to prove that A ⊂ C Since all elements of A i.e. 1 is in set C , A is a subset of C i.e. A ⊂ C 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 . (iii) If A ⊂ B and B ⊂ C, then A ⊂ C Given A ⊂ B and B ⊂ C. Let x ∈ A ⇒ x∈ B ⇒ x∈ C So, if x ∈ A , x∈ C i.e. if an element is in set A, it is ∈ - (belongs to) element in set ⊂ - is a subset A ⊂ B if all elements of A are in B ∴ A is subset of C i.e. A ⊂ C So, given Statement is True

Davneet Singh's photo - Co-founder, Teachoo

Made by

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