$($Discrete Mathematics$)$ Consider the following argument: Hypothesis: If you send me an e$-$mail message, then I will $$nish writing the program. If you do not send me an e$-$mail message, then I will go to sleep early. If I go to sleep early, then I will wake up feeling refreshed. I did not finish writing the program. Conclusion: Therefore, I will wake up feeling refreshed. A$)$ Define propositional variables to represent each of the atomic propositions used above. B$)$ Construct the argument in symbols using the propositional variables you defined in part A$.($Use the Equation Editor to facilitate the symbolic language$).$ C$)$ Show the argument is valid by explaining which rules of inference are used for each step. $($Use the three column table as described in previous exercises, example below.$)$