Question

INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the instructions in the textbook.

Statement 2A. Given the following statement:
(G ⊃ ∼ Q) ≡ ∼(Q • G)
Statement 2A is: Group of answer choices
A) Consistent.
B) Tautologous.
C) Contingent.
D) Logically equivalent.
E) Self-contradictory.

Answer 1

To determine the nature of the given statement, construct a truth table and compare the truth values of each side of the equivalence.

Step-by-step explanation:

The given statement is: (G ⊃ ∼ Q) ≡ ∼(Q • G).

We can construct a truth table to determine the truth values of the statements involved.

We have two variables, G and Q, so we need to consider all possible combinations of truth values for G and Q.

For each combination, we evaluate the truth value of each statement using the logical connectives. Finally, we compare the truth values of the two sides of the equivalence.

If the truth values are the same for all combinations, the statement is a tautology (choice B). Otherwise, it is contingent (choice C).