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
