SOLUTION: 1. P ⊃ (G ⊃ T) 2. Q ⊃ (T ⊃ E) 3. P 4. Q / G ⊃ E 1. ∼S ⊃ D 2. ∼S ∨ (∼D ⊃ K) 3. ∼D / K 1. N ⊃ (J ⊃ P) 2. (J ⊃ P) ⊃ (N ⊃ J) 3. N / P

Algebra ->  Finite-and-infinite-sets -> SOLUTION: 1. P ⊃ (G ⊃ T) 2. Q ⊃ (T ⊃ E) 3. P 4. Q / G ⊃ E 1. ∼S ⊃ D 2. ∼S ∨ (∼D ⊃ K) 3. ∼D / K 1. N ⊃ (J ⊃ P) 2. (J ⊃ P) ⊃ (N ⊃ J) 3. N / P       Log On


   

Question 1201171: 1. P ⊃ (G ⊃ T) 2. Q ⊃ (T ⊃ E) 3. P 4. Q / G ⊃ E

1. ∼S ⊃ D 2. ∼S ∨ (∼D ⊃ K) 3. ∼D / K

1. N ⊃ (J ⊃ P) 2. (J ⊃ P) ⊃ (N ⊃ J) 3. N / P

Need these three problems solved with rules of inference.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


First problem

-------------

1. P-->(G-->T)      Premise

2. Q-->(T-->E)      Premise

3. P                Premise

4. Q                Premise

// show G-->E

5. G-->T            3,1 Modus Ponens (MP)

6. T-->E            4,2 MP

7. G-->E            5,6 Hypothetical Syllogism (HS)

*** done ***





Second problem  (Learn from the other two solutions, and you should

be able to easily fill in steps 4 and 5).  

-----------------------------------------

1. ~S-->D           Premise 

2. ~Sv(~D-->K)      Premise

3. ~D               Premise

// show K 

4.                  3,1 Modus Tollens (MT)

5.                  4,2  Disjunctive Syllogism (DS)

6. K                3,5  Modus Ponens (MP) 

*** done ***



Third problem

-------------

1.  N-->(J-->P)        Premise 

2.  (J-->P)-->(N-->J)  Premise

3.  N                  Premise

// show P

4.  J-->P              3,1 Modus Ponens (MP)

5.  N-->J              4,2 MP

6.  J                  3,5 MP

7.  P                  6,4 MP

*** done ***



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