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338.001/2/4/5/8/22/23/24/25/26/27/28/29, VL / UE Logic, Martina Seidl et al., 2026W
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Given propositional formula
(d ∨ ¬a) ∧ (¬f ∨ ¬c) ∧ (¬b ∨ ¬a) ∧ (e ∨ ¬b) ∧ (¬c) ∧ (a ∨ b ∨ c) ∧ (¬d ∨ e) ∧ (¬e ∨ ¬c)
Which two clauses given in the list below can be derived with one or more applications of the resolution rule?
(Keep in mind that disjunction is commutative, i.e., the order of literals in a clause is irrelevant).
Which of the following rules are applicable on sequent ¬a ∨ b, ¬(a ∧ (¬c ∨ d)), ¬e ⊢ a in the next step?
Given formula φ. Assume that ⊢φ has a derivation in the sequent calculus such that all leaves are axioms. Then φ is ...
| x | y | z | ψ1 | ψ2 | ψ3 |
|---|---|---|---|---|---|
| 0 | 0 | 0 | 0 | 1 | 0 |
| 0 | 0 | 1 | 0 | 1 | 0 |
| 0 | 1 | 0 | 0 | 1 | 0 |
| 0 | 1 | 1 | 0 | 1 | 0 |
| 1 | 0 | 0 | 0 | 1 | 0 |
| 1 | 0 | 1 | 0 | 1 | 0 |
| 1 | 1 | 0 | 0 | 1 | 0 |
| 1 | 1 | 1 | 1 | 1 | 0 |
Which of the following formulas are subformulas of
(¬⊤ ∧ ((a → ¬ (b ∨ ¬c)) ∨ (¬a ∧ b ∨ ¬c)))?
The validity of the formula P → S can also be proven by showing that
The formula (¬x → (y ∧ (¬z ∨ w)) ∨ ¬x) is ...
Which of the following formulas are equivalent to ((¬x → (y ∨ z)) ↔ (x ∨ ¬y)) ?
What do the rules of De Morgan say?
Which of the following formulas are subformulas of (¬x → (y ∧ (¬z ∨ w)) ∨ ¬x)?