Thread: Automata Languages and DFA etc.

Exhibit the languages L1 and L2 such that

L*1 ∩ L*2 ≠ ( L1 ∩ L2 )*

Note: L1 = L base 1 etc

-My attempt-

L1 = {a,b}
L2 = {a,ab}
L1 ∩ L2 = {a}
(L1 ∩ L2)* = {a}*
L1* ∩ L2* =/= {a}*

Is there any problem with my answer or does it needs more work.

Thanks

The answer is fine. Perhaps you can say why L1* ∩ L2* =/= {a}*: e.g., ab ∈ L1* ∩ L2*, but ab ∉ {a}*.