Question $1$: Concurrency $(10$ points$)$

Are the following statements TRUE or FALSE? Justify your answer.

$[$Note: $2$ marks for each question. No marks will be given without explanation.$]$

$($a$)$ A working solution to a concurrency problem on a multiple core system should also be applicable to a single core system; however, the reverse is not necessarily true.

$($b$)$ In the readers$-$writers problem, threads X and Y are allowed to simultaneously access the shared resource if and only if either X and Y are both reading or X and Y are both writing.

$($c$)$ If a thread executes a sem$\_$wait$()$ call on a binary semaphore s $,$ it must eventually execute a sem$\_$post$()$ call on the same semaphore. Failure to do so may result in a synchronization bug.

$($d$)$ If thread X calls cond$\_$signal$()$ before thread Y calls cond$\_$wait$(),$ it allows thread Y to return from cond$\_$wait$()$ without blocking.

$($e$)$ If thread $\backslash ($ X $\backslash )$ calls sem$\_$post$()$ before thread $\backslash ($ Y $\backslash )$ calls sem$\_$wait$(),$ it allows thread $\backslash ($ Y $\backslash )$ to return from sem$\_$wait$()$ without blocking.