Question 1201171
<pre>
First problem
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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).  
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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
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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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