Statement 2F
Given the following statement:
(Q ⊃ ∼ C) • (R ⊃ ∼ Q)
-Statement 2F is:
A) Tautologous.
B) Inconsistent.
C) Contingent.
D) Self-contradictory.
E) Consistent.

Question

Quizplus · Accepted Answer

To determine the truth value of this statement, we need to create a truth table.

Q | R | C | ∼C | ∼Q | Q ⊃ ∼C | R ⊃ ∼Q | (Q ⊃ ∼C) • (R ⊃ ∼Q) 
--|---|---|----|----|---------|---------|------------------
T | T | T |  F |  F |    F    |    F    |        F         
T | T | F |  T |  F |    T    |    F    |        F         
T | F | T |  F |  F |    F    |    T    |        F         
T | F | F |  T |  F |    T    |    T    |        T         
F | T | T |  F |  T |    T    |    T    |        T         
F | T | F |  T |  T |    T    |    T    |        T         
F | F | T |  F |  T |    F    |    T    |        F         
F | F | F |  T |  T |    T    |    T    |        T

The truth table shows that the statement is not a contradiction (there is at least one row where the statement is true), but it is not a tautology either (there are rows where the statement is false). Therefore, the statement is contingent.

Statement 2F Given the Following Statement