Using the rules of inferences deduce the conclusion from the premises : $($show work$)$

a$.$

Show that the hypothesis $"$If you send me an e$-$mail, then I will finish writing the program," $"$If you do not send me an e$-$mail, then I will go to sleep early,", and $"$If I go to sleep early, then I will wake up feeling refreshed" lead to the conclusion $"$If I do not finish writing the program, then I will wake up feeling refreshed."

b$.$

$[((notpvvq)r{)}^{{?}^{?}}(r(svvt){)}^{{?}^{?}}(not{s}^{{?}^{?}}$notu${)}^{{?}^{?}}(notu$nott$)]p.$