decidiability

Question

Which of the following statements is/are true?

I. If L is decidable, L^R may or may not be decidable.
II. If L⊆{0}^*, then L is decidable
III. If L≤_m {0ⁿ 1ⁿ│n≥0}, then L is Decidable

Answer 1

III. If L≤_m {0ⁿ 1ⁿ│n≥0}, then L is Decidable . True L≤_m {0ⁿ 1ⁿ│n≥0}[CFL] CFL is decidable . Decidable goes from right to left so L is also decidable.

https://courses.engr.illinois.edu/cs373/fa2011/exams/fa10midterm2sol.pdf

Comments

What about $2^{nd}$ option?

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And in (3) question, what does $\le_m$ mean?