The Logic Book 6th Edition Sentential Logic Semantics p 104

The Logic Book 6th Edition: Sentential Logic: Semantics, p. 104, q. 3

Construct the corresponding material conditional for each of the following arguments. For each of the arguments, either show that the argument is truth-functionally invalid by constructing an appropriate shortened truth-table for the corresponding material conditional or show that the argument is truth-functionally valid by constructing a full truth-table for the corresponding material conditional.

(A v C) & ~ H

___________

~ C

Solution

A    C     AVC    H not H      (AVC)& not H        not C

T    T      T         T         F                F                          F

T T      T          F        T                T                              F

T    F      T        T        F                 F                               T

T    F      T        F       T                 T                                T

F    T      T        T        F                 F                                 F

F    T      T        F        T                 T                                F

F    F      F        T       F                   F                           T

F   F      F         F      T                    F                            T

Now notice that last two columns are not same.therefore the argument is truth-functionally invalid.