Let $${L_1}$$ recursive language. Let $${L_2}$$ and $${L_3}$$ be languages that are recursively enumerable but not recursive. Which of the following statement is not necessarily true?

Which one of the following languages over the alphabet $$\left\{ {0,\left. 1 \right)} \right.$$ is described by the regular expression $${\left( {0 + 1} \right)^ * }0{\left( {0 + 1} \right)^ * }0{\left( {0 + 1} \right)^ * }$$

The regular expression $${0^ * }\left( {{{10}^ * }} \right){}^ * $$denotes the same set as

Consider the set $$\sum {^ * } $$ of all strings over the alphabet $$\,\sum { = \,\,\,\left\{ {0,\,\,\,1} \right\}.\sum {^ * } } $$ with the concatenation operator for strings