$1-$ Type Inference $(20$ points$)$

$1)$ Suppose we have the following expressions $($we omit some information

and we replace it with #n$,$ where n is some positive integer$).$

a : #$1$ list

b : #$2$

let c $=$ b :: a

let d $=(1,$ true$)$ :: c

where the last expression type checks without error.

$$ What is the type #$1?$

$$ What is the type #$2?$

$$ What is the type of the expression$([$d$])?$

$2)$ Suppose we have the following expressions $($we omit some information

and we replace it with #n$,$ where n is some positive integer$)$:

a : int list

b : #$1$

c : #$2$

let $($x$,$y$)=$ b in $($x :: a$,[$x $+$ y$]$ @ c$)$

where the last expression type checks without error.

$$ What is the type #$1?$

$$ What is the type #$2?$

$$ What is the type of the expression$([[$x$]],$ c :: $[])?$