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

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:

$1.$ Write code that determines if a relation $($R$)$ of ordered pairs is reflexive or not

& then if it is not, finds the reflexive closure of R $($R$*).$ The output should be:

a$)$ R $=\{...\}$

b$)$ R is or is not reflexive

c$)$ R$*$ if it is not reflexive

d$)$ Show the code works for the relation $\{(1,1),(4,4),(2,2),(3,3)\}$ on the

set $\{1,2,3,4\}.$

e$)$ Show the code works for the relation $\{($a$,$a$),($c$,$c$)\}$ on the set $\{$a$,$b$,$c$,$d$\}.$

$2.$ Write code that determines if a relation $($R$)$ of ordered pairs is symmetric or

not & then if it is not, finds the symmetric closure of R $($R$*).$ The output

should be:

a$)$ R $=\{...\}$

b$)$ R is or is not symmetric

c$)$ R$*$ if it is not symmetric

d$)$ Show the code works for the relation $\{(1,2),(4,4),(2,1),(3,3)\}$ on the

set $\{1,2,3,4\}.$

e$)$ Show the code works for the relation $\{(1,2),(3,3)\}$ on the set

$\{1,2,3,4\}.$

$3.$ Write code that determines if a relation $($R$)$ of ordered pairs is transitive or not

& then if it is not, finds the transitive closure of R $($R$*)$ using Warshall$$s

Algorithm. The output should be:

a$)$ R $=\{...\}$

b$)$ R is or is not transitive

c$)$ R$*$ if it is not transitive

d$)$ Show the code works for the relation $\{($a$,$b$),($d$,$d$),($b$,$c$),($a$,$c$)\}$ on the

set $\{$a$,$b$,$c$,$d$\}.$

e$)$ Show the code works for the relation $\{(1,1),(1,3),(2,2),(3,1),(3,2)\}$ on

the set $\{1,2,3\}.$

$4.$ Write code that determines if a relation $($R$)$ of ordered pairs is an equivalence

relation or not and the reason why. The output should be:

a$)$ R $=\{...\}$

b$)$ R is or is not an equivalence relation

c$)$ The reasons why, if it is not an equivalence relation $($i$.$e$.,$ it is not

reflexive, and$/$or it is not symmetric, and$/$or it is not transitive$).$

d$)$ Show the code works for the relation $\{(1,1),(2,2),(2,3)\}$ on the set

$\{1,2,3\}.$

e$)$ Show the code works for the relation $\{($a$,$a$),($b$,$b$),($c$,$c$),($b$,$c$),($c$,$b$)\}$ on

the set $\{$a$,$b$,$c$\}.$

$5.$ Write code that determines if a relation $($R$)$ of ordered pairs is a poset of the

set $($S$)$ or not and the reason why. The output should be:

a$)$ S $=\{...\}$

b$)$ R $=\{...\}$

c$)($S$,$R$)$ is or is not a poset

d$)$ The reason why, if it is not poset $($i$.$e$.,$ it is not reflexive, and$/$or it is

not antisymmetric, and$/$or it is not transitive.

e$)$ Show the code works for the relation $\{(1,1),(1,2),(2,2),(3,3),(4,1),$

$(4,2),(4,4)\}$ on the set $\{1,2,3,4\}.$

f$)$ Show the code works for the relation $\{(0,0),(0,1),(0,2),(0,3),(1,$

$0),(1,1),(1,2),(1,3),(2,0),(2,2),(3,3)\}$ on the set $\{0,1,2,3\}.$