PLEASE DO IT IN PYTHON AND ACTUALLY WRITE THE CODE. THANK YOU!

Label each output with a description, e$.$g$.,1$a$.$ Union of R$1$ and R$2$

$$ Use the methods or functions inherent in the language and$/$or using methods or functions you create. Like previous assignments, don$$t $$hard code$$ a solution you did on paper as the output.

$$ Create a program for the following:

$1.$ For the relations:

R $1=\{(1,1),(2,2),(3,3)\}$ and R$2=\{(1,1),(1,2),(1,3),(1,4)\}$

perform the following set operations and display the results:

a$)$ R$1\backslash$cup R$2$

b$)$ R$1\backslash$cap R$2$

c$)$ R$1$ R$2$

d$)$ R$2$ R$1$

$2.$ Display S $$ R$,$ where:

R is the relation from A $=\{1,2,3\}$ to B $=\{1,2,3,4\}$ with

R $=\{(1,1),(1,4),(2,3),(3,1),(3,4)\}$

S is the relation from B $=\{1,2,3,4\}$ to C $=\{0,1,2\}$ with

S $=\{(1,0),(2,0),(3,1),(3,2),(4,1)\}$

$3.$ For R $=\{(1,1),(1,4),(2,3),(3,1),(3,4)\},$ show R $2.$

$4.$ For the relation R $=\{($x$,$ y$)|$ x $+$ y $=0\}$ on the set $\{-10,...,-1,0,1,...,10\}$:

a$)$ Show R as a set of ordered pairs.

b$)$ Show whether R is reflexive or not.

c$)$ Show whether R is symmetric or not.

d$)$ Show whether R is antisymmetric or not.

e$)$ Show whether R is transitive or not.

$$ Hint: For No$.2$ and $3$ you will need to create a function$/$method that takes the

composite of two relations.