Test 1 - 45 minutes
Question 1. Prove the validity of the sequents below:
a)
q → (p → r), ¬r, q ⊢ ¬p
b)
p → q, r → s ⊢ p ∧ r → q ∧ s
c)
p → q ∧ r ⊢ (p → q) ∧ (p → r)
d)
¬(¬p ∨ q) ⊢ p
Question 2. For the sequents below, show which ones are valid
and which ones aren’t:
a)
⊢ ¬p → (p → (p → q))
b)
p ∧ q ⊢ ¬(¬p ∨ ¬q)
Question 3. Prove the following theorem of propositional logic
(p → q) ∨ (q → r)