* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download (˜P ∨ ˜Q) are tautologically equivalent by constructing a truth
Survey
Document related concepts
Propositional calculus wikipedia , lookup
History of logic wikipedia , lookup
Meaning (philosophy of language) wikipedia , lookup
Jesús Mosterín wikipedia , lookup
Laws of Form wikipedia , lookup
Law of thought wikipedia , lookup
Interpretation (logic) wikipedia , lookup
Non-standard analysis wikipedia , lookup
Truth-bearer wikipedia , lookup
Tractatus Logico-Philosophicus wikipedia , lookup
Propositional formula wikipedia , lookup
Transcript
Truth-Value Analysis [Logic 1: Rabern] University of Edinburgh Truth-tables and tautologies: 1. Show that P ∧ Q and ˜(˜P ∨ ˜Q) are tautologically equivalent by constructing a truthtable. 2. Determine by means of truth-value analysis whether or not the following sentence is a tautology: R ↔ ((R ∨ S) ∧ (R ∨ ˜S)). 3. Determine by means of truth-value analysis whether or not the following sentence is a tautology: R → ((˜S ∧ R) ∨ R). Check by the method of truth tables whether or not the following arguments are valid: 4. P ∨ Q. ∼P ∴ P → Q P Q P ∨ Q ∼P P → Q 5. P → Q. ∼P ∴ ∼Q P Q P → Q ∼P ∼Q 6. (P → Q) ∧ R. ∼R ∨ P ∴ Q P Q R (P → Q) ∧ R ∼R ∨ P Q 7. ∼(P ↔ Q). R → (P ∨ Q) ∴ P ∨ ∼R For each of the following either construct a derivation of the conclusion from the premises or show by the method of truth tables that it is invalid (i.e. provide a countermodel). 8. ˜R → P. ˜S → ˜P. R → S ∴ R 9. ˜Z. (R → ˜Z) → (Q ∧ P ) ∴ (Q ∧ P ) 10. ˜R. P ↔ (R ∧ (P ∨ S)) ∴ P → ˜S 11. ˜((P ↔ Q) ∨ ˜(Q → P )) ∴ ˜Q ∧ P “A tautology leaves open to reality the whole—the infinite whole—of logical space: a contradiction fills the whole of logical space leaving no point of it for reality.” – Wittgenstein