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Fact 1: All...

Question

Fact $1$ : All hats have brims.
Fact $2$ : There are black hats and blue hats.
Fact $3$ : Baseball caps are hats.
If the first three statements are facts, which of the following statements must also be a fact?
I: All caps have brims.
II: Some baseball cars are blue.
III: Baseball caps have no brims.

A

I only

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B

II only

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C

II and III only

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D

None of the statements is a known fact.

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Solution

The correct option is D None of the statements is a known fact.
All baseball caps have brims, since baseball caps are hals(Fact $3$ ) and all hats have brims(Fact $1$ ). This rules out statement III, but it doesn't follow that all caps, a category that may include caps that are not baseball caps have brims(statement I). Statement II cannot be confirmed, either, since it is possible, given the information, that all baseball caps are black.

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