Write the following ML functions using map, foldr or foldl higher$-$order functions. On top of your code Include $3$line comment with your name, purpose and date. Precede each function by a one$-$line comment including exercise number. Save your code as chapter$9.$txt and submit it by canvas.

$1.(6$p$)$ Function multpairs of type: $($int $*$ int$)$ list $\backslash (\backslash$rightarrow $\backslash )$ int list that takes a list of pairs of integers and returns the list of products of pairs. For example: multpairs $[(1,3),(3,7)]$ should return $[3,21].$

$2.(6$p$)$ function max of type int list $\backslash (\backslash$rightarrow $\backslash )$ int that returns the largest element of a given list of integers. Your function need not behave well on empty list. For example: max $[1,2,7,\backslash (\backslash$sim $9]\backslash )$ should return $7.$

$3.(6$p$)$ Function odds of type: int list $\backslash (\backslash$rightarrow $\backslash )$ int list so that odds $\backslash ($ L $\backslash )$ returns the list of all odd numbers in $\backslash ($ L $\backslash )$ in the original order. For example: odds $\backslash ([1,5,2,4,7,0,\backslash$sim $2]\backslash )$ should return $\backslash ([1,5,7]\backslash ).$

$4.(6$p$)$ Function cubes of type int list $\backslash (\backslash$rightarrow $\backslash )$ int list that returns the list of cubes of the numbers in the given list For example: cubes $\backslash ([2,1,\backslash$sim $3,4]\backslash )$ should return $\backslash ([8,1,\backslash$sim $27,64]\backslash ).$

$5.(6$p$)$ Function product of type int list $\backslash (\backslash$rightarrow $\backslash )$ int that returns the product of a list of integers. Your function should return $1$ if the list is empty. For example: product $\backslash ([1,\backslash$sim $2,7,\backslash$sim $4]\backslash )$ should return $56.$