Relationships in Truth Statements

Answers

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
   • Addition 10