🛈 This materials is useful for Unit 1 in CSIR-NET.

True or False: Let A and B be two connected subsets of a metric space. If B is a set such that A ⊆ B ⊆ C, then B is connected.

TRUE

Wrong. Taking counterexamples, let A = {1}, B = {1} U {2}, C = [1,2]. Clearly, the hypothesis is satisfied, but B is not connected.

FALSE

To prove, you need a proof. To disprove, you need a counterexample. Leave your proof below in comments!

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