Since $2023,$ you have been working as a junior software engineer for Core Design, a leading corporation thatdevelops technical solutions for industrial applications. After spending a few months learning the technologyused at Core Design, you were invited to perform work involving the development of solutions for problemsin subject matter fields related to computing. To enable a team of computer engineers to design new technicalsolutions, your supervisor assigned you the role of solving the following questions.Part $1$:Task $1$:Construct a proof of the Five Color TheoremTask $2$:Prepare a power point presentation that explores an application of group theory incomputer sciences. Provide $10-15$ slides, you will not be penalized if you go beyond slidelimit