Q$7$: Consider the following mathematical theory: For all a$,$ b $>0,$ the following is true: a $+$ b $>$ a

and a $+$ b $>$ b$.$ This statement holds for every element $($or combination of elements$)$ set. Using

JUnit Theories:

$1.$ Write a testing program to check the truth of this mathematical statement for every pair

$($every possible combination$)$ of a and b from the value set val$=\{1,2,307,400567\}.$

$2.$ Add another theory to be covered in your testing program in which the commutative feature

of every possible pair of the integers a and b should be true: a $+$ b $=$ b $+$ a$.$ Use the same

value set val as in Task $1$ for this statement as well.

$3.$ Consider a new value set newval$=\{0,-1,-10,-1234,1,10,6789\}$ as your data points

for input values in your testing program for every possible pair of a and b$.$ What will be your

results, and why? Demonstrate and justify your achieved results.

$4.$ Considering the value set newval, rectify your previous testing program using Assumption

to be able to check the truth of the aforementioned mathematical theories over every possible

pair of a and b from the value set newval.

$5.$ Consider another value set:

$1\{0,-1,-10,-1234,1,10,6789,$ Integer.MAX$\_$VALUE, Integer.MIN$\_$VALUE$\}$

as your data points for input values in your testing program for every possible pair of a and

b$.$ What will be your results, and why? Demonstrate and justify your achieved results.