Question 1202690: Are there any mistakes made in solving the following problem? If so, provide the correct answer.
1. W ⊃ Z
2. Z ⊃ (X ∨ Y)
3. Y • W
4. X ⊃ U
5. Y ⊃ V / U ∨ V
6. W 3, Simp
7. W ⊃ (X ∨ Y) 1, 2, HS
8. X ∨ Y 7, 6, MT
9. U ∨ V 4, 5, CD
Answer by RBryant(14)   (Show Source):
You can put this solution on YOUR website! Your answer has problems. You were on the right track at first but then you left out needed details. My derivations will be below the dotted line.
The original question is the following:
1. W ⊃ Z
2. Z ⊃ (X ∨ Y)
3. Y • W
4. X ⊃ U
5. Y ⊃ V / U ∨ V.
--------------------------------------------------
DERIVATION ------------------LINE(S) ------ RULE USED
6. W ------------------------------3 ---------------Simp.(this rule is skipping a step)**
7. W ⊃ (X ∨ Y)-------------------1,2 ---------------H.S.
8. X ∨ Y --------------------------6,7 --------------M.P.(you wrote MT which is wrong.)
9. (X ⊃ U) • (Y ⊃ V)--------------4,5 --------------Conj.
10. U ∨ V -------------------------8,9 --------------C.D.
** The rule of Simplification is sometimes used only on the left side (at least in some logic circles). In other words, we would need to use the commutation rule FIRST and then use Simplification. I used what you wrote down to save time BUT the truth is we would get the same result and not have to write down the extra line in the proof. Just note, in some case we would have to strictly follow every rule and not skip steps at all. [Yes, that means even if we know the result is the same and seems like we are
writing down more than we think we should].
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