IIT Madras MS written test 2019 - TOC - 1

Question

Let L1 and L2 be 2 languages which are not regular. Which of these is true?

1. The union of L1 and L2 is not regular.
2. The intersection of L1 and L2 is not regular.

• A. Both I and II are true
• B. I is true, II is false
• C. I is false, II is true
• D. Both I and II are false

Comments

option D is right

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Both are false.

Counter examples for each can be given.

Answer 1

Let L1=$a^nb^n$  and L2={$a^xb^y$ | x!=y}

1. L1 U L2 : 

L=a*b* which is clearly a Regular Language. Hence I is False.

2. L1 ∩ L2:

L={} which is Regular Language. Hence II is False.

So, (D) Both I and II are False.