Question

Let L be a language given by L = {a^n b^n : n ≥ 0 } , then
L2 is equal to
a) { a^n b^n a^m b^m :n ≥ 0,m ≥ 0 }
b) { a^n b^n :n ≥ 0 }
c) { a^n b^n a^n b^n :n ≥ 0 }
d) none of these.

Answer 1

Answer on Question #42825, Math, Other

Problem. Let $L$ be a language given by $L = \{a^n b^n : n \geq 0\}$, then $L^2$ is equal to

a) $\{a^n b^n a^m b^m : n \geq 0, m \geq 0\}$

b) $\{a^n b^n : n \geq 0\}$

c) $\{a^n b^n a^n b^n : n \geq 0\}$

d) none of these.

Solution.

If $L_1$ and $L_2$ are languages over some common alphabet, then concatenation $L_1L_2$ consists of all strings of the form $vw$ where $v$ is a string from $L_1$ and $w$ is a string from $L_2$.

The language $L^2$ consists of all strings $a^n b^n a^m b^m$, where $n \geq 0$ and $m \geq 0$.

Answer: a) $\{a^n b^n a^m b^m : n \geq 0, m \geq 0\}$

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