Statement Logic and Proofs

# Statement Logic and Proofs - I Proofs in Statement Logic a...

• Notes
• 4

This preview shows pages 1–3. Sign up to view the full content.

I. Proofs in Statement Logic: a. Ex: i. (A.B) ii. (B->(C v D)) iii. ~D iv. :. C v. It can be deduced from (A.B)’s truth that B is true. vi. This means that the antecedent of the second premise is true, and thus the consequent must also be true for the conditional to be true. vii.If the consequent is true, C and D cannot be both false. 1. Furthermore, noting that B -> (C v D), and B is true, (C v D) must be true because this is an instance of Modus Ponens. viii. Now, given that (C v D) MUST be true, and given that ~D is true and thus D is false, it follows that C MUST be true, via the disjunctive syllogism argument form. 1. Thus, the argument is valid. b. (p.q) :. q = “simplification” valid form c. In proofs, valid forms are referred to as inference rules, and are means of deducing steps in a proof. d. Inference rules: i. Modus Ponens ii. Modus Tollens iii. Disjunctive Syllogism 1. p v q, ~p, :. q

This preview has intentionally blurred sections. Sign up to view the full version.

iv. Hypothetical Syllogism 1. p->q, q->r, :. p->r v. Constructive Dilemma 1. p v q, p->r, q->s, :. r v s vi. simplification 1. p.q, :. p vii.Conjunction: 1. p, q, :. p.q viii. Addition: 1. p, :. p v q
This is the end of the preview. Sign up to access the rest of the document.
• Spring '08
• peterhodges
• Logic, inference rules, Rue

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern