Write program in Java or Python. DO NOT create the sequence by adding each element value into the sequence MANUALLY $---$no credit will be given in this case. You have to use the above closed formula to derive elements.

$(2)$ Determine the truth values of $\backslash (\backslash$forall x $\backslash$mathrm$\{$P$\}(\backslash$mathrm$\{$x$\})\backslash )$ and $\backslash (\backslash$exists $\backslash$mathrm$\{$x$\}\backslash$mathrm$\{$P$\}(\backslash$mathrm$\{$x$\})\backslash )$

$\backslash [$

$\backslash$mathrm$\{$P$\}(\backslash$mathrm$\{$x$\})$: $\backslash$mathrm$\{$x$\}>\backslash$text $\{$ input$\_$num $($input$\_$num is a user$-$input integer.$)\}$

$\backslash ]$

Domain of x :

elements from Sequence A

For example, if the input$\_$num $\backslash (=5\backslash )$ then $\backslash (\backslash$mathrm$\{$P$\}(\backslash$mathrm$\{$x$\})$: $\backslash$mathrm$\{$x$\}>5\backslash ).$

Hint: Use Universal Quantifier$-$Conjunction $/$ Existential Quantifier$-$Disjunction to decide the truth values of $\backslash (\backslash$forall x $\backslash$mathrm$\{$P$\}(\backslash$mathrm$\{$x$\})/\backslash$exists x $\backslash$mathrm$\{$P$\}(\backslash$mathrm$\{$x$\})\backslash ).$ DONOT use the functions that come within Python or Java, you have to create your own coding to do that.

$(3)$ Print out the following on the screen:

$($a$)$ First $100$ elements in Sequence A

$($b$)$ "The universal quantifier statement is when inputting number is $\backslash$#$"($True or False in the statement is based on your code results; $\backslash$# is input$\_$num$)$

$($c$)$ "The existential quantifier statement is when inputting number is $\backslash$#$."($True or False in the statement is based on your code results; $\backslash$# is input$\_$num$)$

$(4)$ Calculate sum of the first n elements in Sequence A and convert the number into binary format. Print out the following on the screen:

"The sum of the first n elements in Sequence A is xxx and it's equivalent binary number is xxx $."$

Submitting your project:

You should submit the following files on Canvas:

$1.$ Source code $(.$java or $.$py file$)$

$2.$ Screenshots of TWO examples of different input$\_$num with corresponding output results $($refer to Step$(3)).$

$3.$ Screenshots of TWO examples of different input $\backslash ($ n $\backslash )$ with corresponding output results. $($refer to Step$(4)).$