SOLUTION: Can you please help me complete the following rules by adding the implication rules to each line! Please & Thank you!!!!!!!! Will give u an amazing review :) Problem #1: ~ A v

Question 1031927: Can you please help me complete the following rules by adding the implication rules to each line! Please & Thank you!!!!!!!! Will give u an amazing review :)
Problem #1: ~ A v (B � C), ~ (~ B � A) → ~ C .: ~ A
1. ~ A v (B � C)
2. ~ (~ B � A) → ~ C .: ~ A
3. (~ A v B) � (~ A v C)
4. ~ A v B
5. ~ A v ~ ~ B
6. ~ (A � ~ B)
7. ~ (~ B � A)
8. ~ C
9. ~ A v C
10. ~ A
Problem #2: (M � N) → O, ~ M ↔ ~ L .: L → (N → O)
1. (M � N) → O
2. ~ M ↔ ~ L .: L → (N → O)
3. M → (N → O)
4. (~ M → ~ L) � (~ L → ~ M)
5. ~ M → ~ L
6. L → M
7. L → (N → O)

Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
~ A v (B � C), ~ (~ B � A) → ~ C .: ~ A
1. ~ A v (B � C)---------------------Hypothesis

2. ~ (~ B � A) → ~ C ----------Hypo.
3. (~ A v B) � (~ A v C) ------------Distributivity on #1
4. ~ A v B ------------------------Simplification
5. ~ A v ~ ~ B -----------------------Double negation
6. ~ (A � ~ B) ----------------------de Morgan's law
7. ~ (~ B � A) ---------------------- Commutativity
8. ~ C ---------------------Modus ponens on #2 and #7
9. ~ A v C ---------------------------Simplification from #3
10. ~ A ------------------------Disjunctive syllogism on #8 and #9

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