Question

INSTRUCTIONS: Use an ordinary truth table to answer the following problems. Construct the truth table as per the instructions in the textbook. Statement 1CGiven the following statement: (H ∨ ∼ K) ≡ (K ⊃ H)

Statement 1C is:
A) Self-contradictory.
B) Contingent.
C) Consistent.
D) Logically equivalent.
E) Tautologous.

Answer 1

To determine if Statement 1C ((H ∨ ∼ K) ≡ (K ⊃ H)) is tautologous, contingent, or self-contradictory, we have to construct a truth table analyzing the equivalence between (H ∨ ∼ K) and (K ⊃ H) for all truth value combinations of H and K.

Step-by-step explanation:

To determine the nature of Statement 1C, we need to construct a truth table comparing (H ∨ ∼ K) and (K ⊃ H). Here we will evaluate each logical connector within the statement and then the equivalence of both expressions:

• Let ∼K represent not K
• Let H ∨ ∼ K represent H or not K
• Let K ⊃ H represent K implies H

We will list all possible truth values for H and K and then determine the resulting truth values for ∼ K, H ∨ ∼ K, K ⊃ H, and finally the equivalence (H ∨ ∼ K) ≡ (K ⊃ H). If, in every possible case, the equivalence holds true, then the statement is tautologous. If it is sometimes true and sometimes false, it is contingent. If it can never be true, it is self-contradictory.