A set of premises and a conclusion are given. Use the valid argument forms discussed in this chapter to deduce the conclusion from the premises, giving a reason for each step. Assume all variables are statement variables. (a) p ∨ q (b) q → r (c) p ∧ s → t (d) ~r (e) ~q → u ∧ s (f) ∴t Make selections from the ones below to show the first steps of a proof and the reason for the conclusion.

See deduction below

Step-by-step explanation:

I will use the known inference rules (modus ponens, etc)

From d) and b),

~r

q → r

Therefore ~q (by Modus Tollens)

From a), and our previous conclusion:

p ∨ q

~q

Therefore p (by disjunctive sillogism)

Until know, we have concluded p and ~q. By e)

~q → u ∧ s

~q

Therefore u∧s. (Modus Ponens)

From p, u∧s, and c)

u∧s

s (simplification)

p (previous conclusion)

p∧s (adjuntion)

p∧s→t (Modus Ponens)

Therefore t, as we wanted to conclude.