SOLUTION: Solve the two step proofs below: 1. ~C 2. A > B 3. B > C / ~A 1. D > E 2. F > G 3. D v F / E v G 1. A * B / A v C 1. (H v I) > J 2. H / J 1. (H * I) > J 2.

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Question 1075211: Solve the two step proofs below:
1. ~C
2. A > B
3. B > C / ~A
1. D > E
2. F > G
3. D v F / E v G
1. A * B / A v C
1. (H v I) > J
2. H / J
1. (H * I) > J
2. H
3. I / J
1. H > (I * J)
2. H / J
1. (K * L) v (M * N)
2. ~(K * L) / N
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
1. ~C
2. A > B
3. B > C	/ ~A 
4. ~B                   3,1 modus tollens
5. ~A                   2,4 modus tollens

1. D > E
2. F > G
3. D v F         / E v G     
4. (D > E) * (F > G)    1,2, conjunction
5. E v G                4,3, constructive dilemma

1. A * B	/ A v C   
2. A                    1, simplification
3. A v C                2, addition 

1. (H v I) > J
2. H    	/ J
3. H v I                2,   addition
4. J                    1,3, modus ponens

1. (H * I) > J
2. H
3. I	        / J
4. H * I                2,3 conjunction
5. J                    1,4 modus ponens

1. H > (I * J)
2. H	        / J   
3. I * J                1,2 modus ponens
4. J * I                3,  commutation
5. J                    4, simplification

[Note: that took 3 steps, but perhaps your teacher allows
you to skip commutation, (and perhaps double negation), if
so, you can skip step 4 and make step 5 step 4, with reason 3, simp]

1. (K * L) v (M * N)
2. ~(K * L)	/ N
3. M * N                1,2, disjunctive syllogism
4. N * M                3, commutation
5. N                    4, simplification

[This also took three steps, see note above]

Edwin
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