Conditional Proofs 2

Agenda

1. Quiz
2. Please help me! help you! during office hours if you couldn't do the quiz question.
3. Reset/Taking stock
4. Questions from HW?
5. Affirming the consequent/Denying the antecedent
6. Practice proofs

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



















How to set up a conditional proof:
If you have to solve for a conditional,
1. write the conditional at the bottom of your proof;
2. write the antecedent of the conditional you're trying to prove on the line immediately below the last given premise/assumption OR if there are no premises/assumptions, write it at the top of the proof. Write 'ACP' in the justification column.
3. write the consequent on the line above the conditional you're trying to prove.

Example: 
I'm asked to solve for (P&Q)>Q
Step one: write the conditional at the bottom of your proof
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(P&Q)>Q           CP _____

Step two: write the antecedent of the conditional you're trying to prove on the line immediately below the last given premise/assumption OR if there are no premises/assumptions, write it at the top of the proof. Write 'ACP' in the justification column.

P&Q                  ACP
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(P&Q)>Q          CP

Step three: write the consequent on the line above the conditional you're trying to prove.

P&Q                 ACP
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Q                    ______
(P&Q)>Q       CP

Now that the CP proof has been set up, you solve it the way you'd solve any proof. All you're trying to do is justify Q.


Proofs with CP rule
A.

1. ~C>~A /:. (A&~B)>(~B>C)

B.

1. P>Q
2. ~P>~R /:. ~Q>~R

C. 

1. P
2. ~R    /:.  (P>(~Q>R))>(~S>(T>(Q&~S))

D.

      /:.  P>(~Q>(R>(~S>(R&~S))))

E.  

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