Questions tagged [kleene-star]

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Kleene star operations

Let $𝚺$ be any alphabet and let $𝑳_𝟏 \subseteq 𝚺^{βˆ—}$ and $𝑳_2 \subseteq 𝚺^{βˆ—}$ be two non-empty languages. a. If $𝑳_𝟏 𝚺^{βˆ—} \neq 𝚺^{βˆ—}$ than what can we say about $L_1$. b.Let $\Lambda \...
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Kleene star of L

$L^*$ is the kleene star of L. say we have a def: $L^*$ = $L^0$ U $L^1$ U $L^2$ U ... U $L^K$ then prove that: $L^*$ = $L$ if and only if $L$ = $L$ o $L$ how do i prove this?