Aptitude | GATE CS 1998 | Question 41

Which of the following statement is false?
(A) Every finite subset of a non-regular set is regular
(B) Every subset of a regular set is regular
(C) Every finite subset of a regular set is regular
(D) The intersection of two regular sets is regular


Answer: (B)

Explanation: Taking a counter example, suppose,

L1 = { a^n b^m |n ,m >=0} is always regular
L2 = { a^n b^n | n >=0} is not regular
L1 ⋂ L2 = L2 

L2 which is non regular but L1 is subset of L2.

Therefore Every subset of a regular set is not regular.

Option (B) is correct.

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