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Answer :
Final answer:
The sentences (a) 'Bill has $100' and (b) 'Bill has $50' do not entail each other and are not mutually exclusive. They can both be true if $50 is part of the $100 Bill has, unless specified otherwise. The correct response to the given options is B) No, and they are not mutually exclusive either.
Explanation:
The relationship between the sentences (a) Bill has $100 and (b) Bill has $50 can be analyzed through the concept of entailment. Entailment in this context means that if one statement is true, the other statement must also be true. If Bill has $100, it does not necessarily mean that Bill only has $50, as having $100 implies he could have $50 along with additional money. However, if we only know Bill has $50, we cannot conclude that he has $100, as having $50 does not guarantee that he has additional funds to make up $100.
Based on this logic, statement (a) does not entail statement (b), nor does statement (b) entail statement (a). Also, statements (a) and (b) are not mutually exclusive, as the two statements could be true at the same time if $50 is included in the $100 Bill has. This is true unless it is specified that when mentioning an amount, that amount is exact, and not inclusive of greater sums. In the absence of such specification, we should assume that they are not mutually exclusive.
In conclusion, when presented with the options: A) Yes, B) No, and they are not mutually exclusive either, C) No, but they are mutually exclusive, D) Not enough information given to determine the answer, the most accurate response would be 'B' since the statements are not mutually exclusive and one does not entail the other.
Learn more about entailment here:
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