SOLUTION: Hello, I have a proof I am trying to write up with the following premises: (P^Q)v(R^S) R->L And I am trying to prove ~P->L Here is what I have done so far: |(P^Q)v(R^S)

Question 1147961: Hello,
I have a proof I am trying to write up with the following premises:
(P^Q)v(R^S)
R->L
And I am trying to prove
~P->L
Here is what I have done so far:
|(P^Q)v(R^S)
|R->L
|_
| |P^Q
| |_
| |P
| |PvR
|
| |R^S
| |_
| |R
| |PvR
|PvR
|
| |R
| |_
| |L
| |R^L

If needed I can clarify what rules I am using to justify each step, the last two are the only ones I cannot properly justify. Am I on the right track or completely off? And please let me know if my notation is hard to read/bad form, I want to learn.
Thank you.
Answer by math_helper(2461) (Show Source): You can put this solution on YOUR website!




I am afraid I don't understand your notation at all.  I was taught to always number each line of the proof and to give the logic rule and line number(s) justifying each step.  I like to spell out each rule the first time it is used, and use the abbreviation subsequently (especially here, where the proof is meant to be instructive).  Just the style I've always used, newer methods may be preferred by some instructors.  



Also, there are several different notations & styles possible, I am not familiar with all of them.



Here's how my proof would look:



1. (P^Q)v(R^S)      Premise

2. R-->L            Premise



// Show ~P-->L 



// I will use a conditional proof, I use :: to start conditional proof lines.

// If there was a 3rd premise ~P, you would not need to use a conditional proof.



3. :: ~P            Conditional Proof (CP) assumption #1

4. :: ~Pv~Q         3, Addition (ADD)

5. :: ~(P^Q)        4, DeMorgan's (DeM)

6. :: R^S           5,1 Disjunctive Syllogism (DS) 

7. :: R             6, Simplification (SIMP)

8. :: L             7,2 Modus Ponens (MP)

9. ~P-->L           3-8, CP 







 

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