An enumerator is a $2-$tape DTM connected to a printer. One of its tapes is called the $$work tape$$ and

the other is called the $$print tape$.$ The enumerator has a special state qprint. The computation of an

enumerator proceeds just like a usual $2-$tape DTM$,$ except that it starts with both tapes being empty,

and whenever the enumerator enters state qprint, the $($non$-$blank$)$ content of the print tape is sent to the

printer. A language L is said to be enumerable if there exists an enumerator E such that

$$ For every x in L$,$ E prints x at least once.

$$ For every x $/$ in L$,$ E never prints x$.$

Prove the following statements.

$($a$)$ Every enumerable language is recognizable.

$($b$)$ Every recognizable language is enumerable. For this proof, the following observation might be

useful. An enumerator with k work tapes can be simulated by an enumerator with one work tape,

just like a k tape Turing machine can be simulated by a single tape Turing machine. You do not

have to write the proof of this observation.