Question
Please see if these answers are correct It is just true or false. 1) L 1 , L 2 ( L 1 = L
Please see if these answers are correct
It is just true or false.
1) "L1, L2 (L1 = L2 iff L1* = L2*).
True
(2) "L ((LR)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
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