Natural Deduction Proof 1 YV NSD VD W 2 SDW WVNY NW n YSW 12

Natural Deduction Proof

1 YV [NSD (VD W)] 2 SDW WVNY NW n> YSW 1234/

Solution

Answer :

The premises are given by

Y [ ~ S (V W) ]

S W

W ~ Y

~ W

And the conclusion is ~ V

Proof :

1. S W                               Premise

2. ~ W                                   Premise

3. ~ S                                  ( 1 ) , ( 2 ) , Modus Tollen\'s rule

4. W ~ Y                          Premise

5. ~ Y                                  ( 2 ) , ( 4 ) , Disjunctive Syllogism

6. Y [ ~ S (V W) ]       Premise

7. ~ S (V W )               ( 5 ) , ( 6 ) , Disjunctive Syllogism

8. V W                            ( 3 ) , ( 7 ) , Modus Ponen\'s rule

9. ~ V                                 ( 2 ) , ( 7 ) , Modus Tollens Rule

Thus the conclusion ~ V is logically follows from the given premises