$2.(20$pt$)$ Prove that the following languages are in D $($if you need to define TMs$,$ then clear English

description is sufficient$)$:

$($a$)$ L $=\{|||>10\}.$

$($b$)$ L $=\{|$ M accepts at least three strings starting with a within $10$ steps$\}.$

$($c$)$ L $=\{|$ M does not halt on w within $|$w$|$ steps$\}.$

$($d$)$ L $=\{|$ M$1$ halts on w before M$2$ does, within $|$w$|$ steps$\}.$