Given the statements: J ⊃ B / B ⊃ (N ∨ C) / N ⊃ C / J • ∼C
These statements are:
A) Consistent.
B) Invalid.
C) Inconsistent.
D) Logically equivalent.
E) Tautologous.

Question

Quizplus · Accepted Answer

We can use truth tables to evaluate the consistency of the statements.

J | B | N | C | N ∨ C | B ⊃ (N ∨ C) | J ⊃ B | ∼C | J • ∼C 
T | T | T | T |   T    |        T       |     T      |  F  |     F   
T | T | T | F |   T    |        T       |     T      |  T  |     F  
T | T | F | T |   T    |        T       |     T      |  F  |     F  
T | T | F | F |   F    |        F       |     T      |  T  |     F  
T | F | T | T |   T    |        T       |     F      |  F  |     F  
T | F | T | F |   T    |        T       |     F      |  T  |     F  
T | F | F | T |   T    |        T       |     F      |  F  |     F  
T | F | F | F |   F    |        T       |     F      |  T  |     F  
F | T | T | T |   T    |        T       |     T      |  F  |     F  
F | T | T | F |   T    |        T       |     T      |  T  |     F  
F | T | F | T |   T    |        T       |     T      |  F  |     F  
F | T | F | F |   F    |        F       |     T      |  T  |     F  
F | F | T | T |   T    |        T       |     T      |  F  |     F  
F | F | T | F |   T    |        T       |     T      |  T  |     F  
F | F | F | T |   T    |        T       |     T      |  F  |     F  
F | F | F | F |   F    |        T       |     T      |  T  |     F

From the truth table, we can see that there is no row where all the statements are true. Thus, the statements are inconsistent, and the answer is C.

Given the Statements: J ⊃ B / B ⊃ (N