The document describes 6 statements about formal language theory and asks which are true. It discusses the relationships between regular languages (REG), context-free languages (CF), recursively enumerable languages (RE), and recursively decidable languages (REC) based on the Chomsky hierarchy. According to the solution, statements a, b, c, and d are true, while statements e and f are respectively false and true.

1. Select ALL of the statements below which are TRUE:
a) Consider a language L defined on the alphabet . Assume that there exists a TM M that accepts
L and that halts on any string w in +
. Then the language L is a RE language.
b) For any language L defined on the alphabet , there exists a TM that accepts L.
c) If a language L is REC, then L is RE.
d) Any language L is either REG, DCF, CF, CS, REC, or RE
e) If L is a REG language, then L is also a CF language, CS language, REC language, and RE
language.
f) If L is a CF language, then L is a REC language but L is not a RE language.
Solution
a) Consider a language L defined on the alphabet . Assume that there exists a TM M that accepts
L and that halts on any string w in +. Then the language L is a RE language.
ans)TRUE
b) For any language L defined on the alphabet , there exists a TM that accepts L.
ans)TRUE
with help of chomsky hierarchy we say that every L has TM
c) If a language L is REC, then L is RE.
ans)TRUE
if a language is recursive then it is recursive enumerable
d) Any language L is either REG, DCF, CF, CS, REC, or RE

2. ans)TRUE
why because with help chomsky hierarchy of languages and grammers should be four not more
than that.
e) If L is a REG language, then L is also a CF language, CS language, REC language, and RE
language.
ANS)FALSE
because of chomsky hierarchy of languages and grammers and theeir production rules it is not
true.
f) If L is a CF language, then L is a REC language but L is not a RE language.
ans)TRUE
why because in RE .if we give false input it may or may not halt(loop) but in REC it halts non-
final state for false output and haits in inal state for right input.