LogicMathss

zryyvfn
timer Asked: Jun 1st, 2017

Question Description

CAN ANY OF YOU COMPLETE FIRST 3 QUES IN MAX 30 MINS FROM NOW

I NEED THE FIRST 3 ONLY

Unformatted Attachment Preview

1.1 Qn 1 : Prove the following argument using Indirect Proof (without using Conditional Proof): A ⊢ ¬(B ↔ (A ∧ ¬B)) 1.2 Qn 2 : Prove the following argument using a direct proof (i.e. without using CP or IP): A, ((A ∧ ¬B) → B) ⊢ B 1.3 Qn 3 : Prove the following argument using a direct proof (i.e. without using CP or IP): B ⊢ ¬(B → (A ∧ ¬B)) hint: it’s not easy to see how to start this one. You might find it helpful to think about equivalent formulas to the conclusion, to help you find a path to it! 1.4 Qn 4 : Now prove the original argument, without using Indirect Proof (i.e. either using CP, or by a direct proof): A ⊢ ¬(B ↔ (A ∧ ¬B)) Hint: questions 2 and 3 form the skeleton of a proof for question 4: • Assu e ((A ∧ ¬B) → B) • Derive B • Derive ¬(B → (A ∧ ¬B)) • There y o lude (((A ∧ ¬B) → B)→ ¬(B → (A ∧ ¬B)) by CP, discharging the assumption • It’s fairly easy to complete the proof from here (the formula is equivalent to the conclusion.) You can prove it in a different way if you want!
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