The Gateway to Computer Science Excellence

0 votes

Let $L_{1},L_{2},\cdot\cdot\cdot,L_{k}$ be a collection of languages over alphbet $\Sigma$ such that:

- For all $i\neq j$, $L_{i}\cap L_{j}=\phi$; i.e., no string is in two of the languages.
- $L_{1}\cup L_{2}\cup\cdot\cdot\cdot\cup L_{k} = \Sigma^{\ast}$;i.e., every string is in one of the languages.
- Each of the languages $L_{i}$, for $i=1,2,\cdot\cdot\cdot,k$ is recursively enumerable.

Prove that each of the languages is therefore recursive.

- All categories
- General Aptitude 1.9k
- Engineering Mathematics 7.5k
- Digital Logic 2.9k
- Programming and DS 4.9k
- Algorithms 4.3k
- Theory of Computation 6.2k
- Compiler Design 2.1k
- Databases 4.1k
- CO and Architecture 3.4k
- Computer Networks 4.1k
- Non GATE 1.5k
- Others 1.5k
- Admissions 595
- Exam Queries 576
- Tier 1 Placement Questions 23
- Job Queries 72
- Projects 17

50,644 questions

56,511 answers

195,559 comments

101,073 users