Below, you will find two lists of functions that you may code. You will choose two functions

from the first list $($i$.$e$.$ the "Set Construction" list$)$ and one function from the second list $($i$.$e$.$

the "Set Relations" list$).$ So you will be creating three functions in all. Note that all sets

will be represented by lists in Python with no repeated elements. Also note that there is

a way you can construct sets in Python without using lists. For this assignment,

you are not allowed to use this construction in any way.

Set Construction.

$($a$)$ Create a function called "intersect" whose inputs are two sets $($lists$)$ A and $B,$

and whose output is a set $($list$)$ that is the intersection $AB$ of the two sets.

$($b$)$ Create a function called "union" whose inputs are two sets $($lists$)$ A and $B,$ and

whose output is a set $($list$)$ that is the union $AB$ of the two sets.

$($c$)$ Create a function called "difference" whose inputs are two sets $($lists$)$ A and $B,$

and whose output is a set $($list$)$ that is the set difference $($i$.$e$.$ "set$-$minus"$)\frac{A}{\frac{?}{?}}B$

of the two sets.

$($d$)$ Create a function called "cartesianProduct" whose inputs are two sets $($lists$)A$

and $B,$ and whose output is a set $($list$)$ that is the Cartesian product $AB$

of the two sets. Note that ordered pairs will be represented by lists with two

components.

Set Relations

$($a$)$ Create a function called "subset" whose inputs are two sets $($lists$)$ A and $B,$ and

whose output is a Boolean value. The output is "True" if AsubeB and "False" if

$AB.$

$($b$)$ Create a function called "equal" whose inputs are two sets $($lists$)$ A and $B,$ and

whose output is a Boolean value. The output is "True" if $A=B$ and "False" if

$AB.$ Note that even if $A=B,$ the elements may be listed in a different order.

$($c$)$ Create a function called "element" whose inputs are a set $($list$)$ A and some object.

$x,$ and whose output is a Boolean value. The output is "True" if xinA and "False"

if $x!$inA.

Make sure your function is well documented. You should have one$-$line comments $($using the

single line comments with #$)$ written in complete sentences that describe what each line of

code does. You may not import any packages to help you with your function.