True or false statements.

There are two languages $ L_1 $ Y $ L_2 $ such that $ L_1 $ Y $ L_2 $ are recurvise but $ L_1L_2 $ It is not recursive.

For me, the statements are true because I can describe a non-recursive one (I understood *recursively enumerable*) procedure of two recurring languages.

Test:

Suppose that $ L_1 $ Y $ L_2 $ they are recursive languages Then there is a Turing M1 machine that accepts any input in $ L_1 $ and reject any entry that is not in $ L_1 $. Similarly, there is a Turing M2 machine that accepts any input in $ L_2 $ and reject any entry that is not in $ L_2 $. To determine if $ w ∈ L_1L_2 $, we guess in a non-determining way where to divide the chain into $ w_1w_2 $and run M1 in $ w_1 $ and M2 in $ w_2 $. So, if w is in the language, M1 and M2 will eventually accept.