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Let A, B and C be three sets. If A $ \in $ B and B $ \subset $ C, is it true that A $ \subset $ C? If not, give an example

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No. Let A = {1}, B = {{1}, 2} and C = {{1}, 2, 3}. Here A $ \in $ B as A = {1} and B $ \subset$ C. But A $ \not{\subset}$ C as 1 $ \in $ A and 1 $ \not{\in}$ C.
Note that an element of a set can never be a subset of itself.
answered Jun 12, 2014 by thanvigandhi_1
 

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