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I need help with a propositional logic problem please?

 
 
bobhh
 
Reply Fri 24 Mar, 2017 04:55 pm
1. (P v Q ) & R
2 (R&P) >S
3.(Q&R)>S Conclusion is S

without using conditional proof please?
And perhaps if you have time, please show me the conditional proof method or at least which CP you would use.

Thank you & I do appreciate your time.
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fresco
 
  1  
Reply Sat 25 Mar, 2017 01:41 am
@bobhh,
I would use the method of 'backward fell swoop' in which validity follows, if by taking the conclusion to be false, it renders the premises false.*
In this case, choosing S false clearly gives either Q or R ( or both) false in 3. and P or R false in 2, thereby making 1 false since at least one of Q, P or R must be false. Therefore the argument is valid.

*Refer to the truth table for > to understand this. The premises are a conjunction > the conclusion.
fresco
 
  1  
Reply Sun 26 Mar, 2017 05:55 am
@fresco,
SLIGHT CORRECTION with respect to the falsity of 1...this is not due to 'at least one' of P Q R being false.

If R is true from 2 and 3 then both P and Q must be false making 1 false.
Alternatively if R is false from 2 and 3 then 1 is false.
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