UGC NET CSE | September 2013 | Part 3 | Question: 16

Question

Assume, $L$ is regular language. Let statements $S_1$ and $S_2$ be defined as:

$S_1 : SQRT(L) = \{ x \mid \text{ for some y with } \mid y \mid = \mid x^2 \mid , xy \in L \}$ is regular.

$S_2 : LOG(L) = \{ x \mid \text{ for some y with } \mid y \mid = 2^{\mid x \mid }, xy \in L\}$ is regular.

Which of the following is true?

• A. $S_1$ is correct and $S_2$ is not correct
• B. Both $S_1$ and $S_2$ are correct
• C. Both $S_1$ and $S_2$ are not correct
• D. $S_1$ is not correct and $S_2$ is correct

Answer 1

Answer C) both are not correct

S1: Say x=3 , then y=9 ,xy∊27 which may not in L , but L always contain a multiple of x

S2:Say x=3 , then y=8 , xy∊24 which may not be in L

Comments

what is the meaning of the question?

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The earlier question was so awkward and should have been given marks to all. I corrected it now.