$15$ points What relevant conclusions can be drawn for each set of premises? Use predicates, logical

connectives, and quantifiers to derive conclusions. Explain the rules of inference used to obtain each

conclusion from the premises. If you can't derive a conclusion please state that as well for full credit.

$($a$)"$If I run a marathon, then I$\text{'}$m exhausted the next day." "I drink water if I am exhausted." $"$I

didn't drink any water."

R$.($x$)$: $x$ runs a marathon

$E(x)$:$x$ is exhausted the next day

W$($x$)$: x drinks water

I: Individual, Specifically me

$R(x)E(x)$

$R(I)>E(I)$

notE$(I)$

notR$(I)*$ Modus Tollens

$($b$)$ "Every student has a Discord account." "Rob does not have a Discord account." "Susan has a

Discord account."

$($c$)"$Nll foods that are healthy to cat do not taste yummy." "Tofu is healthy to cat." "You only cat.

what tastes yummy." "You do not eat tofu." "Chocolate bars are not healthy to cat."