Natural Deduction Proof 1 PV NPD MDP MDT SolutionAnswer The

Natural Deduction Proof

Solution

Answer :

The premises are given by

P [ ~P ( M P ) ]

( ~M T ) ~P

( ~M T )

and the conclusion is T

Proof :

1. ( ~M T ) ~P                           Premise

2. ~M T                                  Premise

3. ~P                                            ( 1 ) , ( 2 ) , Modus Ponen\'s rule

4. P [ ~P ( M P ) ]                 Premise

5. ~P ( M P )                           ( 3 ) , ( 4 ) ,Disjunctive syllogism rule

6.   M P                                     ( 3 ) , ( 5 ) , Modus Ponen\'s rule

7    ~M                                          ( 3 ) , ( 6 ) , Modus Tollen\'s rule

8.   T                                             ( 2 ) , ( 7 ) , Modus Ponen\'s rule

hence the conclusion is lofically follows from the given premises.