Create a Lisp recursive function TYPECHECK that takes a list as its parameter and returns a list containing a list of the applicable types (in any order) for each item on the list. The types you should check for are: NIL, T, NUMBER, SYMBOL, LIST and STRING. Do error checking on the input.

[50]> (typecheck '(a b c))

((symbol t) (symbol t) (symbol t))

[51]> (typecheck ())

NIL

[52]> (typecheck '(1 "two" (3 4) ()))

((symbol t number) (string t) (list t) (symbol nil list))

Create a Lisp function FILTERTYPE that takes a type name (see #4) and a list. It should return the list with all items of that type removed. Do error checking on the input.

[67]> (filtertype 'number '(a 2 (3 4) b))

(a (3 4) b)

[72]> (filtertype 'nil '(a () (b c) nil))

(a (b c))

[73]> (filtertype 'blah '(a b c))

Error in FILTERTYPE function. First argument must be a valid type name.