Misc 4 - Chapter 1 Class 11 Sets

Last updated at April 16, 2024 by

Misc 4 - Show that four conditions are equivalent (i) A < B

Misc 4 - Chapter 1 Class 11 Sets - Part 2

Transcript

Misc 4 Show that the following four conditions are equivalent: (i) A ⊂ B (ii) A – B = Φ (iii) A ∪ B = B (iv) A ∩ B = A Showing Condition (i) is equivalent to Condition (ii). Let A ⊂ B This means all elements of A are in B, So, A has no element different from B ⇒ A – B = Φ Showing Condition (ii) is equivalent to Condition (iii). A – B = ∅ This means A has no elements different from B So, all elements of A are in B So, A ∪ B = B ⊂ - is a subset A ⊂ B if all elements of A are in B (i) A ⊂ B (ii) A – B = Φ (iii) A ∪ B = B (iv) A ∩ B = A Showing Condition (iii) is equivalent to Condition (iv). A ∪ B = B This means all elements of A are in B, So , the common elements of A and B must be the elements of A So, A ∩ B = A Thus, (i) ⇔ (ii) ⇔ (iii) ⇔ (iv) Thus, all the four conditions are equivalent.

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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, Social Science, Physics, Chemistry, Computer Science at Teachoo.