GO Classes Test Series 2024 | Mock GATE | Test 11 | Question: 61

GO Classes asked Jan 13 • retagged Jan 13 by Lakshman Bhaiya

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Which of the following is/are undecidable?

$L=\left\{\langle M\rangle \mid M\right.$ is a TM, $\mathrm{L}(M) \neq \emptyset$, and $\left.\mathrm{L}(M) \neq \Sigma^*\right\}$.
$\{\langle M\rangle \mid M$ is a TM and $\mathrm{L}(M)=\varnothing\}$
$\mathrm{L}=\{\langle\mathrm{M}>| \mathrm{M}$ is a TM and $\mathrm{L}(\mathrm{M})$ is uncountable $\}$
$L=\{\langle M\rangle \mid M$ is a DFA and $L(M)$ is uncountable $\}$

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GO Classes asked Jan 13 • retagged Jan 13 by Lakshman Bhaiya

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GauravRajpurohit

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https://www.youtube.com/watch?v=atrZdsQU5RE Time stamp 2:26:30

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$ \large{\colorbox{yellow}{Detailed video solution of this question with direct time stamp}}$
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EVERY language is countable. So, Option C $\&$ D are trivial properties (trivially false), hence countable.

GO Classes answered Jan 13 • edited Jan 13 by Lakshman Bhaiya

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✌ Edit necessary (rajan31 “"hence decidable"”)

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