For S € (0+1)* let d(s)denote the decimal value of s(e.g.d(101)= 5).Let L = {s € (0 + 1) | d (s) mod 5 = 2 and d (s) mod 7 != 4)}Which one of the following statements is true?
A)L is recursively enumerable, but not recursive
B)L is recursive, but not context-free
C)L is context-free, but not regular
D)L is regular

Question

Quizplus · Accepted Answer

The language L is defined by two conditions based on the decimal value of a binary string: it must leave a remainder of 2 when divided by 5, and it must not leave a remainder of 4 when divided by 7. However, the condition that a number must leave a remainder of 2 when divided by 5 can be represented by a finite automaton, as the set of such numbers is periodic with a period of 5. Similarly, the condition that a number must not leave a remainder of 4 when divided by 7 does not affect the regularity of the language, as excluding a specific remainder out of 7 possible outcomes can also be represented with a finite automaton. Therefore, the combination of these conditions still results in a language that can be recognized by a finite automaton, making L a regular language.

For S € (0+1)* Let D(s)denote the Decimal Value of S(e.g.d(101)=