Question

Q1: Which of the following claims are true?* 1 point The recognizable languages are closed under union and intersection The decidable lanquages are closed under union and intersection The class of undecidable languages contains the class of recognizable anguages For every language A, at least one of A or A*c is recognizable Other: This is a required question Q2: Which of the following languages are recognizable? (Select all that apply) 1 point EDFA-{ «A> 1 A is a DFA and L(A) is empty } ALL-DFA = { <A> IA is a DFA over Sigma and L(A) = Sigma* } The complement of E_DFA ETM (<M>| M is a TM and L(M) is empty ) The complement of ETM Other: This is a required question Q3: Select all the true statements below.* 1 point If a language L and complement of L are both recognizable, then they are both decidable ATM is undecidable but not Turing recognizable ATM is undecidable and Turing recognizable The complement of A TM is Turing recognizable This is a required question

Answer 1

Q1) Second and fourth option are the correct answers.

The recognizable languages are closed under intersection but not under union.

The decidable languages are closed under union, complement and intersection.

For recognizable languages TM halts and and accepts the strings in that language and for other strings it either rejects or does not halt. A language is decidable only if there is a Turing Machine that accept strings in the language and reject strings not contained in that language.

For every language A either A or A^c is recognizable.

Q2) First and fourth option are the correct answers.

E_DFA = {<A>| A is a DFA and L(A) is empty} is recognizable.

E_TM = {<M>| M is a TM and L(M) is empty} is recognizable.

Q3) First and third options are the correct answers.

If a language and the complement of that language are both recognizable,then they are both decidable.

A_TM is undecidable and Turing recognizable.

Hope this helps.