Prove the following identity on languages A, B: (A ∪ B)* = (AB)* For string x, the reversal of x, denoted $x^R$, is defined as , if x= $varepsilon$; and as $x_n$ $x_2$ $x_1$, if x= $x_1$ $x_2$...$x_n$. For language A, the reversal of A, denoted $A^R$, is defined to be $A^R$ = { $x^R$ for all x in A }. Determine if the following equation is true for all languages A or not. Present a proof or a counterexample: ($A^R$)* = $(A*)^R$ I still don't really understand what the star symbol means and how that affects the equations.

Discrete Structures question. Don't know how to start really rusty, please explain like I'm five.

Prove the following identity on languages A, B: (A ∪ B)* = (AB)*
For string x, the reversal of x, denoted $x^R$, is defined as , if x= $varepsilon$; and as $x_n$ $x_2$ $x_1$, if x= $x_1$ $x_2$…$x_n$. For language A, the reversal of A, denoted $A^R$, is defined to be
$A^R$ = { $x^R$ for all x in A }.
Determine if the following equation is true for all languages A or not. Present a proof or a counterexample: ($A^R$)* = $(A*)^R$

I still don’t really understand what the star symbol means and how that affects the equations.

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