SOLUTION: Construct Conditional Proofs 1. P → Q 2. (P � Q) → R 3. P → (R → S) 4. (R � S) → T / P → T (Hint: This is a long proof!)

Question 193061: Construct Conditional Proofs

1. P → Q
2. (P � Q) → R
3. P → (R → S)
4. (R � S) → T / P → T (Hint: This is a long proof!)

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!

1. P → Q
2. (P � Q) → R
3. P → (R → S)
4. (R � S) → T / P → T
-----------------------
5.   P                               Assumption
6.   Q                        1,5    Modus Ponens
7.   P � Q                    5,6    Conjunction 
8.   R                        2,7    Modus Ponens
9.   P � R                    5,8    Conjunction
10.  (P � R) -> S               3    Exportation
11.  S                       10,9    Modus Ponens
12.  R � S                   8,11    Conjunction
13.  T                       4,12    Modus Ponens
14.  P -> T                  5,13    Conditional Proof

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SOLUTION: Construct Conditional Proofs 1. P &#8594; Q 2. (P � Q) &#8594; R 3. P &#8594; (R &#8594; S) 4. (R � S) &#8594; T / P &#8594; T (Hint: This is a long proof!)

SOLUTION: Construct Conditional Proofs 1. P → Q 2. (P � Q) → R 3. P → (R → S) 4. (R � S) → T / P → T (Hint: This is a long proof!)