# Automata Theory Questions and Answers – Union, Intersection & Complement

This set of Automata Theory Multiple Choice Questions & Answers (MCQs) focuses on “Union, intersection and complement of Regular Language & Expression”.

1. Regular sets are closed under union,concatenation and kleene closure.
a) True
b) False
c) Depends on regular set
d) Can’t say

Explanation: Regular sets are closed under these three operation.

2. Complement of a DFA can be obtained by
a) making starting state as final state
b) no trival method
c) making final states non-final and non-final to final
d) make final as a starting state

Explanation: String accepted in previous DFA will not be accepted and non accepting string will be accepted .

3. Complement of regular sets are _________
a) Regular
b) CFG
c) CSG
d) RE

Explanation: Regular sets are closed under complement operation.

4. If L1 and L2 are regular sets then intersection of these two will be
a) Regular
b) Non Regular
c) Recursive
d) Non Recursive

Explanation: Regular expression are also colsed under intersection.

5. If L1 is regular L2 is unknown but L1-L2 is regular ,then L2 must be
a) Empty set
b) CFG
c) Decidable
d) Regular

Explanation: Regular is closed under difference.
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6. Reverse of a DFA can be formed by
a) using PDA
b) making final state as non-final
c) making final as starting state and starting state as final state
d) None of the mentioned

Explanation: By making final state as starting state string starting from end will be accepted.

7. Reverse of (0+1)* will be
a) Phi
b) Null
c) (0+1)*
d) (0+1)

Explanation: There is only one state which is start and final state of DFA so interchanging starting start and final state doesn’t change DFA.

8. A ___________ is a substitution such that h(a) contains a string for each a.
a) Closure
b) Interchange
c) Homomorphism
d) Inverse Homomorphism

Explanation: This operation replace using a function .

9. Homomorphism of a regular set is _______
a) Universal set
b) Null set
c) Regular set
d) Non regular set

Explanation: Regular set are closed under homomorphism.

10. (a ^ 5b ^ 5)* is example of ________
a) Type 0 language
b) Type 1 language
c) Type 2 language
d) Type 3 language

Explanation: It is a regular expression.

11. Which of the following is type 3 language ?
a) Strings of 0’s whose length is perfect square
b) Palindromes string
c) Strings of 0’s having length prime number
d) String of odd number of 0’s

Explanation: Only d is regular language.

12. a ^ nb ^ n where (n+m) is even .
a) Type 0
b) Type 1
c) Type 2
d) Type 3

Explanation: It is a regular expression.

13. Complement of a ^ nb ^ m where n >= 4 and m <= 3 is example of
a) Type 0
b) Type 1
c) Type 2
d) Type 3

Explanation: It is a regular expression.

14. a ^ nb ^ m where n >= 1, m >= 1, nm >= 3 is example of
a) Type 0
b) Type 1
c) Type 2
d) Type 3

Explanation: It is a regular expression.

15. Complement of (a + b)* will be
a) phi
b) null
c) a
d) b

Explanation: Given expression accept all string so complement will accept nothing.

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