The following question on the theory of computation is GATE 2019 CS question 24:

For $Σ = \{a, b\}$, let us consider the regular language: $$L = \{x \mid x = a^{2+3k} \text{ or } x = b^{10+12k}, k \geq 0\}$$ Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for $L$?

 

(A) 3$\quad$(B) 5$\quad$(C) 9$\quad$(D) 24

###My Attempt

I tired to solve like this. I divide the minimum string possible into $x(y^i)z$ that is $a^2$ so getting i value $2$ but option not available.

Then I take second minimum $a^5$ i.e., taking $x=\epsilon$ and $y=a^5$ and $z=\epsilon$.

I am getting $i=5$. So is it correct answer??

The following question on the theory of computation is GATE 2019 CS question 24:

For $Σ = \{a, b\}$, let us consider the regular language: $$L = \{x \mid x = a^{2+3k} \text{ or } x = b^{10+12k}, k \geq 0\}$$ Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for $L$?

(A) 3$\quad$(B) 5$\quad$(C) 9$\quad$(D) 24

My Attempt

I tired to solve like this. I divide the minimum string possible into $x(y^i)z$ that is $a^2$ so getting i value $2$ but option not available.

Then I take second minimum $a^5$ i.e., taking $x=\epsilon$ and $y=a^5$ and $z=\epsilon$.

I am getting $i=5$. So is it correct answer??

The question is from GATE 2019 CS:

For $Σ = \{a, b\}$, let us consider the regular language: $$L = \{x \mid x = a^{(2+3k)} \text{ or } x = b^{(10+12k)}, k \geq 0\}$$ Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for $L$?

(A) 3
(B) 5
(C) 9
(D) 24

###My Attempt:

I tired to solve like this. I divide the minimum string possible into $x(y^i)z$ that is $a^2$ so getting i value $2$ but option not available.

Then I take second minimum $a^5$ i.e., taking $x=E$ and $y=a^5$ and $z=E$.

I am getting $i=5$. So is it correct answer??

The following question on the theory of computation is GATE 2019 CS question 24:

For $Σ = \{a, b\}$, let us consider the regular language: $$L = \{x \mid x = a^{2+3k} \text{ or } x = b^{10+12k}, k \geq 0\}$$ Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for $L$?

(A) 3$\quad$(B) 5$\quad$(C) 9$\quad$(D) 24

###My Attempt

I tired to solve like this. I divide the minimum string possible into $x(y^i)z$ that is $a^2$ so getting i value $2$ but option not available.

Then I take second minimum $a^5$ i.e., taking $x=\epsilon$ and $y=a^5$ and $z=\epsilon$.

I am getting $i=5$. So is it correct answer??

The question is from GATE 2019 CS:

For $Σ = \{a, b\}$, let us consider the regular language: $$L = \{x | > x = a^{(2+3k)} or x = b^{(10+12k)}, k \geq 0\}$$ Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for $L$?

(A) 3
(B) 5
(C) 9
(D) 24

###My Try:

I tired to solve like this. I divide the minimum string possible into $x(y^i)z$ that is $a^2$ so getting i value $2$ but option not available.

Then I take second minimum $a^5$ i.e., taking $x=E$ and $y=a^5$ and $z=E$.

I am getting $i=5$. So is it correct answer??

The question is from GATE 2019 CS:

For $Σ = \{a, b\}$, let us consider the regular language: $$L = \{x \mid x = a^{(2+3k)} \text{ or } x = b^{(10+12k)}, k \geq 0\}$$ Which one of the following can be a pumping length (the constant guaranteed by the pumping lemma) for $L$?

(A) 3
(B) 5
(C) 9
(D) 24

###My Attempt:

I tired to solve like this. I divide the minimum string possible into $x(y^i)z$ that is $a^2$ so getting i value $2$ but option not available.

Then I take second minimum $a^5$ i.e., taking $x=E$ and $y=a^5$ and $z=E$.

I am getting $i=5$. So is it correct answer??