Use inference rules to deduce the following conclusions from the following sets of premises: a) Premises: p ∨ q q → r, p ∧ s → t, ¬r, ¬q → u ∧ s Conclusion: t b) Premises: (p ∧ t) → (r ∨ s), q → (u ∧ t), u → p, ¬s Conclusion: q → r

a. Solution for - Premises: p ∨ q, q → r, p ∧ s → t, ¬r, ¬q → u ∧ s Conclusion: t

By arriving at the conclusion "t", the argument is proven.

∴ The premise and conclusion is valid.

b. Solution for - Premises: (p ∧ t) → (r ∨ s), q → (u ∧ t), u → p, ¬s Conclusion: q → r

Since the above argument includes a proposition "q", the argument above will be valid, if the argument with the following premise and conclusion below is valid.

Knowing this, we can rewrite
Premises: (p ∧ t) → (r ∨ s)
q → (u ∧ t)
u → p
¬s
Conclusion: q → r
as
Premise: (p ∧ t) → (r ∨ s)
q → (u ∧ t)
u → p
¬s
q
Conclusion: r

Observe the two propositions and how they differ from each other. If we can prove that the second proposition is valid, it automatically means that the first (original) proposition is also valid.