$4.$ Discuss in technical detail whether or not the following argument is valid:

$$Are CFLs decidable$$ is reducible to $$Are TMs decidable$$ and since TMs are not decidable, then neither are CFLs$.$

$5.$ Given the alphabet $\backslash$Sigma $=\{0,1\},$ give a detailed technical argument as to whether the set of all languages over $\backslash$Sigma is countable or not.

$6.$ The Sipser text $($pp$.279-281)$ shows that A $=\{0$k$1$k$|$k $>=0\}$ in TIME$($nlogn$).$ It then claims $($p$.281)$ that $$any language that can be decided in o$($nlogn$)$ time on a single tape TM is regular.$$ Explain how these facts can be consistent. $($As part of the discussion, use the Pumping Lemma for regular languages to show that A is not regular.$)$