Apparently, if ${\sf P}={\sf NP}$, all languages in ${\sf P}$ except for $\emptyset$ and $\Sigma^*$ would be ${\sf NP}$-complete.Why these two languages in particular? Can't we reduce any other language in ${\sf P}$ to them by outputting them when accepting or not accepting?
If P = NP, why wouldn't $\emptyset$ and $\Sigma^*$ be NP-complete?
complexity theory;np complete;reductions