Form a detailed argument that proves the propositions in the following Prompts. Make sure your
response addresses all the items in the associated rubric on Canvas. Make sure to correctly utilize
and reference definitions and theorems from the textbook [1] as you develop your response. These
writing prompts are heavily inspired by problems in the course textbook [1].
The stability of SFC, a beautiful city nestled by a bay, is governed by the quantities of two energy
sources B79X49 and R99a0y. SFC is stable when the quantity of B79X49 is greater than the
quantity of R99a0y. The quantities of these energies for any given day are symbolized as b and r,
respectively. Initially, b > r, and b and r are positive integers.
For as long as the inhabitants of the area have been around, there has been a general feeling of
unrest that is due to the fact that b > r. They hope for a day of stability and have monitored how the
energy quantities transition from one day to the next for a long time. Based on their observations,
after each day, exactly one of four things happens:
• Energy Transition 1: r increase by 1 unit.
• Energy Transition 2: b decreases by 1 unit.
• Energy Transition 3: b increases by 1 unit and r increases by 2 units.
• Energy Transition 4: b decreases by 2 units and r decreases by 1 unit.
A group of concerned citizens predicted that if there is ever a day when b

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