Question

Use an ordinary truth table to answer the following problem.

Given the following statement:
(N ⊃ K) ≡ (K ⊃ N)
The statement is:
a) contingent
b)tautologous
c)self contradictory

Answer 1

The logical status of the statement (N ⊃ K) ≡ (K ⊃ N) is determined to be contingent after constructing a truth table and evaluating all possible truth values of N and K. The equivalence does not hold true in all scenarios, thus it is not a tautology or a contradiction.

Step-by-step explanation:

The problem asks us to determine the logical status of the statement (N ⊃ K) ≡ (K ⊃ N) using a truth table. To achieve this, we will list all possible truth values of the individual propositions N and K, determine the truth values of (N ⊃ K) and (K ⊃ N) for each combination, and then check if the equivalence (≡) holds true in all cases. In classical logic, (N ⊃ K) is true whenever N is false or both N and K are true, and similarly, (K ⊃ N) is true whenever K is false or both K and N are true.

• N true, K true: (N ⊃ K) is true, (K ⊃ N) is true, equivalence is true.
• N true, K false: (N ⊃ K) is false, (K ⊃ N) is true, equivalence is false.
• N false, K true: (N ⊃ K) is true, (K ⊃ N) is false, equivalence is false.
• N false, K false: (N ⊃ K) is true, (K ⊃ N) is true, equivalence is true.

Since the equivalence is not true in all cases, the statement is not tautologous. It is also not self-contradictory, as there are cases where the equivalence is true. Therefore, the statement is considered to be contingent, meaning its truth depends on the truth values of N and K.