Question 9230 – GATE 2007
January 24, 2024Question 9235 – GATE 2007
January 24, 2024Question 9231 – GATE 2007
Which of the following is TRUE?
Correct Answer: B
Question 7 Explanation:
If a set is finite then it must be regular , as every language which contains finite elements is regular. Hence, every finite subset of a non-regular set is regular.
Every subset of regular set is regular, is false. For example L = {an bn | n ≥ 0} is subset of ∑* and L is CFL, whereas ∑* is regular. Hence, every subset of regular set need not be regular.
The union of two non-regular sets is not regular, is also a false statement.
For example, consider two CFL’s.
L = {an bn | n ≥ 0} and its complement Lc = {am bn | m ≠ n } U b*a*.
If we take UNION of L and Lc , we will get ∑*, which is regular. Hence the UNION of two non-regular set may or may not be regular.
The statement, Infinite union of finite sets is regular is also a false statement.
Every subset of regular set is regular, is false. For example L = {an bn | n ≥ 0} is subset of ∑* and L is CFL, whereas ∑* is regular. Hence, every subset of regular set need not be regular.
The union of two non-regular sets is not regular, is also a false statement.
For example, consider two CFL’s.
L = {an bn | n ≥ 0} and its complement Lc = {am bn | m ≠ n } U b*a*.
If we take UNION of L and Lc , we will get ∑*, which is regular. Hence the UNION of two non-regular set may or may not be regular.
The statement, Infinite union of finite sets is regular is also a false statement.
Every subset of a regular set is regular.
Every finite subset of a non-regular set is regular.
The union of two non-regular sets is not regular.
Infinite union of finite sets is regular.