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Derive ~M

1.~R & ~W.

2.[(R=W)v(Mv G)]=>(W=M).

As you see, the tableaux is valid.So l want to translate it an SL derivation(Fitch style)

Here is my understanding

1 ~R. 1 => E

2 ~W. 1 => E

3|-[(R=W)v(MVG)]. 2=>E

4 |--(R=W). 3.Assume

5 | R. Assume

6.| W. 4-6 =E

7 W. 4-7 V I

8.|—-(MVG). Assume ?

Any help would be appreciated.

5
  • From not-R and not-W derive R=W and use or-intro to derive the antecedent of 2nd premise, from which derive W=M. With not-W, derive not-M. Mar 12, 2021 at 17:23
  • Thanks l did it in my notes
    – Eudoxus
    Mar 12, 2021 at 17:55
  • I’m voting to close this question because this is not a homework forum Mar 13, 2021 at 10:59
  • It is not a home work problem! @SwamiVishwananda. I am 58 and graduated Concordia U in 1993😡
    – Eudoxus
    Mar 13, 2021 at 15:23
  • Who downvoted me -1 ? Please upvote me
    – Eudoxus
    Mar 13, 2021 at 15:23

1 Answer 1

0

The first five lines say: Assume M under the premises, and there derive ~R and ~W (we do this by conjunction elimination). Well, in fitch you put the premise first, then raise the assumption.

Now the left branch of line 6 says (R = W) v (M v G) must be derivable (under the assumptions) since assuming it to be false leads to contradictions on all paths. So we shall derive it.

Since we do not have a way to derive M or G, we look to deriving R = W by biconditional introduction, then using disjunction introduction and finally condition elimination

This brings us to the right branch of your line 6, which says a contradiction can be derived from here, and indeed having derived M = W, M, and ~W we can do so (hint: biconditional elimination). And having derived a contradiction under the assumption of M, we use negation introduction to discharge the assumption and so deduce its negation: ~M

  |  ~R & ~W
  |_ [(R = W) v (M v G)] > (W = M)
  |  |_ M
  |  |  ~R
  |  |  ~W
  |  |  :
  |  |  :
  |  |  :
  |  |  :
  |  |  :
  |  |  :
  |  |  R = W
  |  |  (R = W) v (M v G)
  |  |  W = M
  |  |  :
  |  |  :
  |  |  #
  |  ~M
2
  • Wow, thanks for the answer
    – Eudoxus
    Mar 19, 2021 at 21:51
  • Why did l get downvoted
    – Eudoxus
    Mar 19, 2021 at 23:48

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