Fill in the blanks with the valid form of inference that is being used and the lines the inference follows from. Note: the conclusion is written to the right of the last premise, following the “/?“ symbols.

Question

Example 1:
1. M ? ~N
2. M
3. H ? N /? ~H
4. ~N Modus ponens, 1, 2
5. ~H Modus tollens, 3, 4
Example 2:
1. A v B
2. C ? D
3. A ? C
4. ~D /? B
5. A ? D Hypothetical syllogism, 3, 2
6. ~A Modus tollens, 5, 4
7. B Disjunctive syllogism, 1, 6

# 1
1. A ? C /? (A v E) ? (C v D)
2. A _________________
3. C _________________
4. A v E _________________
5. C v D _________________
6. (A v E) ? (C v D) ______________
# 2
1. A ? (B ? D)
2. ~D
3. D v A /? ~B
4. A _________________
5. B ? D _________________
6. ~B _________________
# 3
1. A ? ~B
2. A v C
3. ~~B ? D /? C
4. ~~B _________________
5. ~A _________________
6. C _________________
#4
1. A ? B
2. A ? ~D
3. B ? C /? C ? ~D
4. A _________________
5. A ? C _________________
6. C _________________
7. ~D _________________
8. C ? ~D _________________
#5
1. C
2. A ? B
3. C ? D
4. D ? E /? E v B
5. C ? E _________________
6. C v A _________________
7. E v B _________________
#6
1. (A v M) ? R
2. (L ? R) ? ~R
3. ~(C ? D) v (A v M) /? ~(C ? D)
4. ~R _______________
5. ~(A v M) _______________
6. ~(C ? D) _______________
#7
1. (H ? K) ? L
2. ~R ? K
3. K ? (H v R) /? L
4. K _________________
5. H v R _________________
6. ~R _________________
7. H _________________
8. H ? K _________________
9. L _________________
#8
1. C ? B
2. ~D ? ~B
3. (A ? (B ? C)) v D
4. A v C /? B ? C
5. ~D _________________
6. A ? (B ? C) _____________
7. ~B _________________
8. ~C __________________
9. A __________________
10. B ? C __________________
11. ~B __________________
12. (B ? C) v B __________________

Answer 1

1.
Simplification 1
Simplification 1
Addition 2
Addition 3
Conjunction 4, 5
2.
Disjunctive syllogism 2, 3
Modus ponens 1, 4
Modus tollens 2, 5
3.
Simplification 3
Modus tollens 1, 4
Disjunctive syllogism 2, 5
4.
Simplification 2
Hypothetical syllogism 1, 3
Modus ponens 4, 5
Simplification 2
Conjunction 6, 7
5.
Hypothetical syllogism 3, 4
Addition 1
Constructive dilemma 2, 5,
6
6.
Simplification 2
Modus tollens 1, 4
Disjunctive syllogism 3, 5
7.
Simplification 2
Modus ponens 3, 4
Simplification 2
Disjunctive syllogism 5, 6
Conjunction 4, 7
Modus ponens 1, 8
8.
Simplification 2
Disjunctive syllogism 3, 5
Simplification 2
Modus tollens 1, 7
Disjunctive syllogism 4, 8
Modus ponens 6, 9
Modus tollens 8, 10
Addition 10