Please use python to write the code. Thanks

Create a program for the following:

$1.$ Prove $($true$)$ or disprove $($false$)$ the following assertions for the domain of

$\{0,1,2,3,4,5,6,7,8,9,10\}.$ For the universal quantifier, show at least one of the

numbers in the domain that disproves the assertion. For the existential

quantifier, show at least one number in the domain that proves the assertion:

a$)$x P$($x$),$ where P$($x$)$ is the statement $$x$<2$

b$)$x P$($x$),$ where P$($x$)$ is the statement $$x$<2$

c$)$x $($P$($x$)$ Q$($x$))$ where P$($x$)$ is the statement $$x$<2$ and where Q$($x$)$ is the statement $$x$>7$

d$)$x $($P$($x$)$ Q$($x$))$ where P$($x$)$ is the statement $$x$<2$ and where Q$($x$)$ is the statement $$x$>7$

e$)$ Prove De Morgan$$s Law for the Existential Quantifier where P$($x$)$ is the statement $$x$<5$

f$)$ Prove De Morgan$$s Law for the Universal Quantifier where P$($x$)$ is the statement $$x$<5$

$2.$ Find the following truth values for P$($x$,$y$)$: x $$ y $=1$ where the domain of x and y is $\{1,2,4,5,10,0\mathrm{.}5,0\mathrm{.}25,0\mathrm{.}2,0\mathrm{.}1\}.$ Show the values in the domain that either make the assertions true or false.

a$)$x$$yP$($x$,$y$)$

b$)$x$$yP$($x$,$y$)$

c$)$y$$xP$($x$,$y$)$

d$)$x$$yP$($x$,$y$)$

e$)$y$$xP$($x$,$y$)$

f$)$x$$yP$($x$,$y$)$

$$ Print out a line between each of the above indicating which number your program is answering, $($e$.$g$.,1$b$).$

$$ Remember:

o To prove $$ requires showing it is true for ALL values in the domain; to

prove $$ requires showing it is true for only ONE value in the domain; to

disprove $$ requires showing it is false for ONE value in the domain; to

disprove $$ requires showing it is false for ALL values in the domain.

o To prove Laws, requires showing both sides are the same for the domain

$($either both TRUE or both FALSE$)$; and given P$($x$),$ you have to figure out

what $$P$($x$)$ is$,$ e$.$g$.,$ if P$($x$)=$ x $>$ y$,$ then $$P$($x$)=$ x $<=$ y$.$

$$ Provide comments that explain what each line of code is doing