Define the following $($standard prelude$)$ library functions using recursion.

Note: since these are automatically loaded when you start GHCi, you can verify that your recursive definitions have the same behavior as the corresponding library function $-$ but you will also need to rename your function to avoid a naming clash, e$.$g$.,$ renaming and to and'.

Also: note that most of these functions are defined in the prelude using other library functions rather than using explicit recursion, and are generic functions rather than being specific to lists but they will still work on any instance that your recursive definition works on $($because they are more generic$).$

$($a$)($ A$).$ The and :: $[$Bool$]$ Bool function, which decides if all logical values in a list are True.

$($b$)(1).$ The concat :: $[[$a$]][a]$ function, which concatenates a list of lists.

$($c$)3).$ The replicate :: Int $a[a]$ function, which produces a list with $n$ identical elements.

$($d$)$ The elem : : Eq a $=>a[a]$ Bool function, which decides is a value is an element of a list.