Statements:All bottles are glasses.No cup is a glass. Conclusions:I. No bottle is a cup.II. At least some glasses are bottles.if only conclusion I follows.if only conclusion II follows.if either conclusion I or conclusion II follows.if neither conclusion I nor conclusion II follows.if both conclusion I and conclusion II follow.
Question
Statements:All bottles are glasses.No cup is a glass. Conclusions:I. No bottle is a cup.II. At least some glasses are bottles.if only conclusion I follows.if only conclusion II follows.if either conclusion I or conclusion II follows.if neither conclusion I nor conclusion II follows.if both conclusion I and conclusion II follow.
Solution 1
The answer is: if both conclusion I and conclusion II follow.
Here's the step by step reasoning:
Statement 1: All bottles are glasses. This means that every bottle is also a glass.
Statement 2: No cup is a glass. This means that there is no overlap between cups and glasses.
Conclusion I: No bottle is a cup. Since all bottles are glasses and no cup is a glass, it follows that no bottle can be a cup. So, conclusion I follows.
Conclusion II: At least some glasses are bottles. Since all bottles are glasses, it is true that some glasses are bottles. So, conclusion II also follows.
Therefore, both conclusions I and II follow.
Solution 2
The answer is: if both conclusion I and conclusion II follow.
Here's the step by step reasoning:
Statement 1: All bottles are glasses. This means that every bottle is also a glass.
Statement 2: No cup is a glass. This means that there is no overlap between cups and glasses.
Conclusion I: No bottle is a cup. Since all bottles are glasses and no cup is a glass, it follows that no bottle can be a cup. So, conclusion I follows.
Conclusion II: At least some glasses are bottles. Since all bottles are glasses, it is true that some glasses are bottles. So, conclusion II also follows.
Therefore, both conclusions I and II follow.
Solution 3
The answer is: if both conclusion I and conclusion II follow.
Here's the step by step reasoning:
Statement 1: All bottles are glasses. This means that every bottle is a glass. So, if something is a bottle, it is also a glass.
Statement 2: No cup is a glass. This means that there is no overlap between cups and glasses. If something is a cup, it cannot be a glass.
Conclusion I: No bottle is a cup. Since all bottles are glasses and no cup is a glass, it follows that no bottle can be a cup. So, conclusion I follows.
Conclusion II: At least some glasses are bottles. Since all bottles are glasses, it follows that at least some glasses are bottles. So, conclusion II also follows.
Therefore, both conclusions I and II follow from the given statements.
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