SOLUTION: Can you please assist me with these problems? We are using the Rules of Inference and the Rules of Replacement and I am very confused about the Replacement Rules.Thank you very muc

Algebra ->  Proofs -> SOLUTION: Can you please assist me with these problems? We are using the Rules of Inference and the Rules of Replacement and I am very confused about the Replacement Rules.Thank you very muc      Log On


   

Question 926966: Can you please assist me with these problems? We are using the Rules of Inference and the Rules of Replacement and I am very confused about the Replacement Rules.Thank you very much!
#1-
Q=>(W * D) premise
Q=>W conclusion
#2-
I v (N * F) premise
I => F premise
F conclusion
#3-
P=>A premise
Q=>B premise
(P v Q) => (A v B) conclusion

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to get you started.

I'm using these rules here
https://www.blinn.edu/brazos/humanities/avoelkel/logic%20note%20sheet.pdf

# 1 
1.  Q -> (W * D)
/   Q -> W
-------------------------------------------------------
2.  ~Q v (W * D)                  1      Material Implication
3.  (~Q v W) * (~Q v D)           2      Distribution
4.  ~Q v W                        3      Simplification
5.  Q -> W                        4      Material Implication


Note: Material Implication and Distribution are rules of replacement while Simplification is a rule of inference.

What's the difference? A rule of inference applies to the WHOLE line. A rule of replacement can apply to a piece of a line which means it is easier to apply. Notice how simplification would NOT work on line 1 because it's a rule of inference. You would need line 1 to be W*D in order for simplification to work.

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