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Question Number 208367 by Mastermind last updated on 13/Jun/24

$$1.\mathrm{Find}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{each}\mathrm{of}\mathrm{the}\mathrm{following}$$$$\left(\mathrm{a}\right)\{\mathrm{x}:-3<\mathrm{x}<7\}$$$$\left(\mathrm{b}\right)\{\mathrm{x}:2⩽\mathrm{x}⩽6\}\cup \{-3⩽\mathrm{x}⩽-1\}$$$$\left(\mathrm{c}\right)\{\mathrm{x}:-2⩽\mathrm{x}<5\}\cup \{1<\mathrm{x}⩽7\}$$$$$$$$2.\mathrm{Let}\mathrm{I}=(\mathrm{a},\mathrm{b}).\mathrm{Prove}\mathrm{that}\mathrm{I}\mathrm{is}\mathrm{measurable}$$$$\mathrm{and}\mathrm{m}\left(\mathrm{I}\right)=\mathrm{L}\left(\mathrm{I}\right).$$

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