Disjunctive Syllogism

Agenda

1. Exam: 
1. If you didn't do as well as you would have liked 
2. (a) what was your attendance record? Did you take advantage of office hours and review sessions?
3. (b) What percentage of the homework did you complete?
4. (c) What can I do to help? 
2. Disjunctive Syllogism and 'v' Introduction.
3. Proofs

Exam

Surprising Results!!!!

Students who scored less than 80% on the test also had 80% or lower attendance rates. The lower the score, the lower the attendance rate. It's almost as though the two are related...

1. If you didn't do as well as you would have liked: 
2. (a) what was your attendance record? Did you take advantage of office hours and review sessions?
3. (b) What percentage of the homework did you complete?
4. (c) What can I do to help? 

Disjunctive Syllogism 

Basic Rule: 

1. PvQ              A
2. ~P/~Q          A
3. Q/P              DS

In natural language: 

1. Either you want PIZZA or you want QUOLA.
2. You don't want PIZZA/You don't want QUOLA.
3. You want QUOLA/You want PIZZA.

Adding complexity (but same rule):

A.

1. (P&Q)v(P>Q)  A
2. ~(P>Q)             A
3. P&Q                 DS

B. 

1. ((A<>~B)>(C>~B))v~((~DvC)>(C<~~D))      A
2. what would I need in order to derive                A
3. ((A<>~B)>(C>~B))                                          DS

Fun Activity!!!

In your groups create at least two natural language arguments using DS then symbolize it.

'v' Introduction

Basic Rule:

A. 

1. P                                                  A
2. PvQ (where Q can be anything) v Int

B. Let's kick it up a notch....BAAAM!!

1. P                                        A
2. Pv(P<>((~Q>R)&(SvT))  vInt

In natural language:

1. I'm going to study LOGIC tonight.                 A
2. I'm going to study LOGIC tonight or I'm going to order a PIZZA, drink BEER, and WATCH Trailer Park Boys.                                                       vInt

Fun Activity!!!

In your groups create at least 2 vInt arguments in natural language then symbolize it.

Proofs

A. 

1. P
2. (PvQ)>R   /R

B. 

1. (A&B)
2. (C>E)>~((A&B)v(~C>D))   /:. (C>E)

C. 

1. (~P<>Q)&~R
2. (((~P<>Q)&~R)v(((~T&S)v~P>~T)<>((S&U)>V)v(~T<>R)))>P
3. P>Q                /:. Q

D. 

1. (A>B)v(~C&D)
2. ~(A>B)   /:.  ~C