Example 11 Let A, B and C be three sets. If A ∈ B and B ⊂ C, is it true that A ⊂ C?. If not, give an example. Given: A, B, C are three sets A ∈ B and B ⊂ A To show: A ⊂ C or not? Proof: We will prove this with the help of an example. Let A = {1} B = {{1}, 2, 3} C = {{1}, 2, 3, 4, 5} Here, A ∈ B as set A is an element of set B Also, B ⊂ C as C contains all elements of B But A ⊄ C because 1 ∈ A but 1 ∉ C

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

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