Consider the following sets:
- S1: Set of all recursively enumerable languages over the alphabet {0, 1}.
- S2: Set of all syntactically valid C programs.
- S3: Set of all languages over the alphabet {0, 1}.
- S4: Set of all non-regular languages over the alphabet {0, 1}.
Which of the above sets are uncountable?
(A) S1 and S2
(B) S3 and S4
(C) S1 and S4
(D) S2 and S3
Answer: (B)
Explanation:
- Recursively enumerable languages are countable.
- Syntactically valid C program can be represented with CFG. CFG generates CFL, CFL is countable.
- All languages over {0, 1} may not be countable, because they may also lie in the region of 2Σ*.
- Set of regular languages are countable, non-regular languages may not be countable.
Option (C) is true.
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