Statement 2H
Given the following statement:
[N ∨ ∼ (K ∨ G)] ≡ [(G ⊃ N) • (K ⊃ N)]
-Statement 2H is:
A) Inconsistent.
B) Contingent.
C) Consistent.
D) Self-contradictory.
E) Tautologous.

Question

Quizplus · Accepted Answer

To determine the consistency of the statement, we can use truth tables:

N|K|G|K∨G|~(K∨G)|G⊃N|K⊃N|[N∨~(K∨G)]|[(G⊃N)•(K⊃N)]
-|-|-|----|-------|-----|-----|----------|--------------
T|T|T|  T |   F   |  T  |  T  |     T    |      T       
T|T|F|  T |   F   |  T  |  T  |     T    |      T      
T|F|T|  T |   F   |  T  |  T  |     T    |      T     
T|F|F|  F |   T   |  F  |  T  |     T    |      F    
F|T|T|  T |   F   |  F  |  F  |     T    |      F     
F|T|F|  T |   F   |  T  |  F  |     T    |      F    
F|F|T|  T |   F   |  T  |  T  |     T    |      F    
F|F|F|  F |   T   |  T  |  T  |     T    |      T

Both sides of the statement have the same truth values, which indicates that the statement is true in all cases and is therefore a tautology.

Statement 2H Given the Following Statement