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Question 1200104: When using rules of implication for natural deduction, how would I get to my next steps after the following:
1.(R>L)>(L>~F)
2. ~F v (R>L)
3. ~~F /~R
P.S.: There should be four more steps following those three, I'm just not quite positive of how to move forward from here.
Answer by Edwin McCravy(20054)   (Show Source):
You can put this solution on YOUR website!
1.(R>L)>(L>~F)
2. ~F v (R>L)
3. ~~F /~R
4. R>L 2,3, Disjunctive Syllogism ---That's [(p v q) & ~p]>q
5. L>~F 1,4, Modus Ponens ---That's [(p>q) & p]>q
6. R>~F 4,5, Hypothetical Syllogism ---That's [(p>q) & (q>r)]>(p>r)
7. ~R 6,3, Modus tollens ---That's [(p>q) & ~q]>~p
They're all common sense if you think about it and think about them in words
using "the first", "the second" and "the third", like this:
Disjunctive Syllogism says: [(p v q) & ~p]>q
If you know that (you have the first OR the second) AND (you do NOT have the
first), then you MUST have (the second).
I think of " > " as the same as the word "guarantees".
Modus Ponens says: [(p>q) & p]>q
If you know that (the first guarantees the second), AND you know that you have
(the first), then you MUST have (the second).
Hypothetical Syllogism says: [(p>q) & (q>r)]>(p>r)
If you know that (the first guarantees the second) AND (the second guarantees
the third), then (the first MUST guarantee the third).
Modus Tollens says: [(p>q) & ~q]>~p
If you know that (the first guarantees the second) and (you do NOT have the
second), then (you MUST NOT have the first).
Edwin
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