Please see if these answers are correct

It is just true or false.

1) "L₁, L₂ (L₁ = L₂ iff L₁* = L₂*).

True

(2) "L ((L^R)^R = L).

True

"L₁, L₂ ((L₁ L₂)* = L₁* L₂*).

False. Counterexample: Let L1 = {a} and L2 = {b}. Then (L1L2)* = (ab), while L1 L2* = {a}{b} = {, a, aa, ...} {, b, bb, ...} = {, a, b, aa, ab, bb, ...}.

(4) "L₁, L₂ ((L₁*L₂*L₁*)* = (L₂ L₁)*).

True

(5) "L₁, L₂ ((L₁ L₂)* = L₁* L₂*).

True

(6) "L₁, L₂, L₃ ((L₁ L₂) L₃ = (L₁ L₃) (L₂ L₃)).

True

(7) "L₁, L₂ ((L₁ - L₂) = (L₂ - L₁)).

False. Counterexample: Let L1 = {a} and L2 = {b}. Then L1 - L2 = {a} and L2 - L1 = {b}, so they are not equal.

(8) "L₁, L₂, L₃ ((L₁ L₂) L₃ = (L₁ L₃) (L₂ L₃)).

False. Counterexample: Let L1 = {a}, L2 = {b}, and L3 = {c}. Then (L1L2) L3 = {ab} {c} = {ab, c}, while (L1 L3) (L2 L3) = {a, c} {b, c} = {ac, bc, abc}.

(9) "L ((L*)⁺ = L⁺).

True