Final answer:
The statement (H ∨ ∼ K) ≡ (K ⊃ H) is logically equivalent. You can construct a truth table to verify this. By listing all possible combinations of truth values for the variables H and K, and evaluating the logical operations, you will find that the statement is always true.
Step-by-step explanation:
The statement (H ∨ ∼ K) ≡ (K ⊃ H) is logically equivalent. To construct a truth table for this statement, we need to list all possible combinations of truth values for the variables H and K. There are four possibilities: HH, HK, KH, and KK. We can substitute in the truth values for each combination and use logical operators to evaluate the statement. The truth table will have columns for H, K, (H ∨ ∼ K), (K ⊃ H), and the final equivalence. After filling in all the truth values and performing the logical operations, we find that the final equivalence column has the same truth values for all rows, indicating that the statement is logically equivalent.
Truth table:
H
K
(H ∨ ∼ K)
(K ⊃ H)
Equivalence
T
T
T
T
T
T
F
T
T
T
F
T
F
F
T
F
F
T
T
T