formal logic

snvmry
timer Asked: Apr 20th, 2018

Question Description

Question 1

Use truth tables to prove that the following propositional formulas have the corresponding properties. In each case, also explain (in words) why the formula has the relevant property.

(i) (p ∧ (q ∨ r)) → ((p ∧ q) ∨ r) is valid (ii) (p ∧ ¬q) ↔ (¬p ∨ q) is unsatisfiable

(iii) (p → p) → (q ∧ (q → p)) is satisfiable and is falsifiable (20)

Question 2

Prove that the formulas given in Question 1 (i) and (ii) above have the corresponding properties, by means of semantic arguments in terms of the truth values of formulas. (20)

Question 3

Prove the following theorem: Given a set of formulas U and a single formula A, U |= A iff U ∪ {¬A} is unsatisfiable. (20)

Question 4

Prove that the propositional formulas given in Question 1 (i), (ii) and (iii) above have the corresponding properties, by means of semantic tableaux. (30)

Normally, you shouldn’t use the optimized tableau algorithm described in Section 2.6.4, but you may do so for part (ii) of this question. It will make the tableau shorter and simpler.

Question 5

Prove that the formula given in Question 1 (i) above is a theorem of the Gentzen system

User generated content is uploaded by users for the purposes of learning and should be used following Studypool's honor code & terms of service.

This question has not been answered.

Create a free account to get help with this and any other question!

Related Tags

Brown University





1271 Tutors

California Institute of Technology




2131 Tutors

Carnegie Mellon University




982 Tutors

Columbia University





1256 Tutors

Dartmouth University





2113 Tutors

Emory University





2279 Tutors

Harvard University





599 Tutors

Massachusetts Institute of Technology



2319 Tutors

New York University





1645 Tutors

Notre Dam University





1911 Tutors

Oklahoma University





2122 Tutors

Pennsylvania State University





932 Tutors

Princeton University





1211 Tutors

Stanford University





983 Tutors

University of California





1282 Tutors

Oxford University





123 Tutors

Yale University





2325 Tutors