Natural Deduction Proof 1 EVNY 2 NYDINED NPY 3 NE SolutionAn

Natural Deduction Proof

Solution

Answer :

The premises are given by

1. E ~Y

2. ~Y [ ~ E ( N Y ) ]

3. ~ E

The conclusion is    ~ N

Proof :

1. E ~Y                             Premise

2. ~ E                                   Premise

3. ~ Y                                   ( 1 ) , ( 2 ) Disjuctive syllogism rule

4. ~Y [ ~ E ( N Y ) ]     Premise

5. ~ E ( N Y )                ( 3 ) , ( 4 ) Modus Ponen\'s rule

6.    N Y                           ( 2 ) , ( 5 ) Modus Ponen\'s rule

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

hence ~ N is logically follows from the given premises