A: Romulus is smarter than Remus.
B: Remus is dumb.

Question

BlackTom AI · Accepted Answer

To analyze the relationship between statements A and B, we examine what each asserts and whether one logically implies the other.
Option 1: 'B entails A' — This would mean that from 'Remus is dumb' we could conclude 'Romulus is smarter than Remus.' This is not valid, because 'Remus is dumb' does not specify any comparative information about Romulus relative to Remus. There could be many situations in which Remus is dumb while Romulus is not necessarily smarter, or where Romulus and Remus are both not clearly distinguished in intelligence. Therefore, B does not entail A.
Option 2: 'Neither A nor B entails the other.' — This claims there is no logical implication between the two statements. Given the content, A says Romulus is smarter than Remus, while B says Remus is dumb. While these are related in terms of assessing Remus and Romulus, neither statement logically forces the truth of the other: R being dumb does not necessarily establish that Romulus is smarter than Remus (it could be that both are not smart, or that Romulus is smarter for reasons not captured by B). Conversely, A does not strictly entail that B is true or false; it's possible to interpret 'smarter than' without declaring the absolute level of Remus's intelligence. Hence, the correct relationship is that neither entails the other.
Option 3: 'They are paraphrases.' — Paraphrases would mean both statements express the same content in different words. They do not: A compares two individuals, stating a relative property, while B asserts a simple attribute about Remus. They are not equivalent in meaning, so they are not paraphrases.
Option 4: 'A entails B' — This would mean from 'Romulus is smarter than Remus' we can deduce 'Remus is dumb.' But 'smarter than' does not automatically translate into an outright claim that Remus is dumb; Remus could be intelligent but still less than Romulus, or could be not categorically dumb. The truth of A does not force B. Therefore A does not entail B.
In summary, none of the direct entailments hold between A and B, and the most accurate description among the options is that neither A nor B entails the other. This aligns with the given answer indicating that the correct relation is that neither entails the other.

LING 200 A Quiz 5 (Semantics & Sign lang)

A: Romulus is smarter than Remus. B: Remus is dumb.

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