###### Question 11817 – UGC NET CS 2014 June-paper-3

June 2, 2024###### Question 8731 – Engineering-Mathematics

June 3, 2024# Question 8144 – Theory-of-Computation

Consider the following two statements:

I. If all states of an NFA are accepting states then the language accepted by the NFA is Σ*.

II. There exists a regular language A such that for all languages B, A∩B is regular.

Which one of the following is **CORRECT**?

Correct Answer: B

Question 39 Explanation:

Statement I is false:

The reason is NFA doesn’t have dead state, so even though all states are final state in NFA, the NFA will reject some strings.

For ex:

Consider L = a*b*

The NFA would be:

Even though all states are final states in above NFA, but it doesn’t accept string “aba”.

Hence its language can’t be ∑*.

Statement II is true:

Since A= Φ is a regular language and its intersection with any language B will be Φ (which is regular).

The reason is NFA doesn’t have dead state, so even though all states are final state in NFA, the NFA will reject some strings.

For ex:

Consider L = a*b*

The NFA would be:

Even though all states are final states in above NFA, but it doesn’t accept string “aba”.

Hence its language can’t be ∑*.

Statement II is true:

Since A= Φ is a regular language and its intersection with any language B will be Φ (which is regular).

Only

**I**is trueOnly

**II**is trueBoth

**I**and**II**are trueBoth

**I**and**II**are false
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