Computer Science Engineering (CSE) Exam > Computer Science Engineering (CSE) Questions > Which of the following statements is false?a)...
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Which of the following statements is false?
- a)Every NFA can be converted to an equivalent DFA
- b)Every non-deterministic Turing machine can be converted to an equivalent deterministic Turing machine
- c)Every subset of a recursively enumerable set is recursive
- d)none
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
Which of the following statements is false?a)Every NFA can be converte...
A language is recursively enumerable if there exists a Turing machine that accepts every string of the language, and does not accept strings that are not in the language. Strings that are not in the language may be rejected or may cause the Turing machine to go into an infinite loop.
A recursive language can't go into an infinite loop, it has to clearly reject the string, but a recursively enumerable language can go into an infinite loop.
So, every recursive language is also recursively enumerable. Thus, the statement ‘Every subset of a recursively enumerable set is recursive’ is false.
Thus, option (C) is the answer.
A recursive language can't go into an infinite loop, it has to clearly reject the string, but a recursively enumerable language can go into an infinite loop.
So, every recursive language is also recursively enumerable. Thus, the statement ‘Every subset of a recursively enumerable set is recursive’ is false.
Thus, option (C) is the answer.
Most Upvoted Answer
Which of the following statements is false?a)Every NFA can be converte...
False Statement: Every subset of a recursively enumerable set is recursive.
Explanation:
To understand the statement, we need to first understand what is meant by recursively enumerable and recursive sets.
Recursively Enumerable Set: A set is recursively enumerable if there exists a Turing machine that can list out all the elements of the set. In other words, if an element belongs to the set, the Turing machine will eventually halt and accept that element.
Recursive Set: A set is recursive if there exists a Turing machine that can decide whether or not an element belongs to the set. In other words, the Turing machine will eventually halt and accept or reject the element.
Now, let's look at the statement in detail.
a) Every NFA can be converted to an equivalent DFA: This statement is true. It is a well-known fact that every NFA (nondeterministic finite automaton) can be converted to an equivalent DFA (deterministic finite automaton).
b) Every non-deterministic Turing machine can be converted to an equivalent deterministic Turing machine: This statement is also true. There exists a technique called the subset construction, which can be used to convert any non-deterministic Turing machine to an equivalent deterministic Turing machine.
c) Every subset of a recursively enumerable set is recursive: This statement is false. It is possible to have a subset of a recursively enumerable set that is not recursive. For example, the set of all Turing machines that halt when given an empty input is recursively enumerable, but its complement (the set of all Turing machines that do not halt when given an empty input) is not recursive.
d) None: This option is not the correct answer as option c is false.
Therefore, the false statement is c) Every subset of a recursively enumerable set is recursive.
Explanation:
To understand the statement, we need to first understand what is meant by recursively enumerable and recursive sets.
Recursively Enumerable Set: A set is recursively enumerable if there exists a Turing machine that can list out all the elements of the set. In other words, if an element belongs to the set, the Turing machine will eventually halt and accept that element.
Recursive Set: A set is recursive if there exists a Turing machine that can decide whether or not an element belongs to the set. In other words, the Turing machine will eventually halt and accept or reject the element.
Now, let's look at the statement in detail.
a) Every NFA can be converted to an equivalent DFA: This statement is true. It is a well-known fact that every NFA (nondeterministic finite automaton) can be converted to an equivalent DFA (deterministic finite automaton).
b) Every non-deterministic Turing machine can be converted to an equivalent deterministic Turing machine: This statement is also true. There exists a technique called the subset construction, which can be used to convert any non-deterministic Turing machine to an equivalent deterministic Turing machine.
c) Every subset of a recursively enumerable set is recursive: This statement is false. It is possible to have a subset of a recursively enumerable set that is not recursive. For example, the set of all Turing machines that halt when given an empty input is recursively enumerable, but its complement (the set of all Turing machines that do not halt when given an empty input) is not recursive.
d) None: This option is not the correct answer as option c is false.
Therefore, the false statement is c) Every subset of a recursively enumerable set is recursive.
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Which of the following statements is false?a)Every NFA can be converte...
As recursive enumerable is not a super set of recursive so some recursive enumerable is recursive but not all recursive enumerable is recursive
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Which of the following statements is false?a)Every NFA can be converted to an equivalent DFAb)Every non-deterministic Turing machine can be converted to an equivalent deterministic Turing machinec)Every subset of a recursively enumerable set is recursived)noneCorrect answer is option 'C'. Can you explain this answer?
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