Two propositions are logically equivalent when they share the same truth value in all possible circumstances. A joint truth table reveals this by showing matching columns for the two statements on every row. Logical equivalence means that each proposition implies the other, so they stand or fall together. Accordingly, the relationship described in the stem is that of logical equivalence.
Option A:
Option A is correct because logical equivalence formalises the idea of identical truth behaviour across all valuations. This relation can also be expressed using a biconditional, reflecting mutual implication. The truth-table condition in the question is the standard test for such equivalence.
Option B:
Option B, contradictory, would require that one proposition be true whenever the other is false and vice versa. This implies opposite truth values on every row, not identical ones. Therefore contradiction is not what the stem describes.
Option C:
Option C, inconsistent, typically refers to a set of propositions that cannot all be true together. It does not describe a relation between two single propositions having matching truth values under all conditions. Hence inconsistent is not appropriate here.
Option D:
Option D, independent, suggests that the truth of one proposition has no fixed effect on the truth of the other, so their truth values are not reliably correlated. This is the opposite situation to having identical truth values on every row.
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