reduction$).$ Answer per item$]$ Let A and $B$ be the

$($mapping

$(1$a$)$ If $B$ is decidable then A the following items:

$(1$b$)$ If $A$ is decidable the A must be decidable.

$(1$c$)$ If $B$ is in $P,$ then $B$ must be decidable.

$(1$d$)$ If $A$ is in $P,$ then A must be in $P.$

Let $A,B$ an $P,$ then $B$ must be in $P.$

Let $A,B$ and $L$ be languages. Answer True or False for the following items:

$(1$e$)$ If both A and $B$ are NP$-$complete, then we have both $A{?}_{P}B$ and $B{?}_{P}A.$

$(1$f$)$ If $\frac{?}{\text{b}\text{a}\text{r}}(L)$ is not recognizable, then both $L$ and $\frac{?}{\text{b}\text{a}\text{r}}(L)$ are not decidable.

Answer: