$($a$)(2$ points$)$ True or False: the number of true arithmetical statements involving

positive integers, $+,\backslash$times $,(,)$ and $=$ is countable, i$.$e$.(17+31)\backslash$times $2=96.$ Defend

your answer.

$($b$)(2$ points$)$ True or False: There is at least one language L such that L is decidable,

but some subset B of L is not decidable. Defend your answer.

$($c$)(2$ points$)$ True or False: There exists a bijection from the set of all Turing

machines to the set of natural numbers. Defend your answer