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

Question

Quizplus · Accepted Answer

The statements are consistent. We can use a truth table to show that all the statements can be true at the same time.
Q | N | S | L | B | E | Q ⊃ (N ∨ S) | N ⊃ (L ⊃ B) | (S ∨ E) ⊃ (Q ⊃ B) | Q ≡ ∼ B |
--|---|---|---|---|---|-----------------|---------------|-------------------|-------------|
T | T | F | T | F | T |        T        |       T        |         T         |      F      |
T | T | F | T | F | F |        T        |       T        |         F         |      F      |
T | T | F | F | F | T |        T        |       T        |         T         |      F      |
T | T | F | F | F | F |        T        |       T        |         T         |      F      |
T | F | T | T | F | T |        T        |       T        |         T         |      F      |
T | F | T | T | F | F |        T        |       T        |         F         |      F      |
T | F | T | F | F | T |        T        |       T        |         T         |      F      |
T | F | T | F | F | F |        T        |       T        |         T         |      F      |
F | T | F | T | T | T |        T        |       T        |         T         |      T      |
F | T | F | T | T | F |        T        |       T        |         F         |      T      |
F | T | F | F | T | T |        T        |       T        |         T         |      T      |
F | T | F | F | T | F |        T        |       T        |         T         |      T      |
F | F | T | T | T | T |        T        |       T        |         T         |      T      |
F | F | T | T | T | F |        T        |       T        |         F         |      T      |
F | F | T | F | T | T |        T        |       T        |         T         |      T      |
F | F | T | F | T | F |        T        |       T        |         T         |      T      |

As we can see from the truth table, there is at least one combination of truth values for each statement that makes all the statements true at the same time. Therefore, the statements are consistent.

Given the Statements: Q ⊃ (N ∨ S) / N