Direction: The logic problems in this set present you with three true statements : Fact 1, Fact 2, and Fact 3. Then, you are given three more statements (labeled I, II, and III), and you must determine which of these, if any, is also a fact. One or two of the statements could be true; all of the statements could be true; or none of the statements could be true. Choose your answer based solely on the information given in the first three facts.
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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 caps are blue.
III. Baseball caps have no brims.
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- I only
- II only
- I, II, and III
- None of the statements is a known fact.
Correct Option: D
All baseball caps have brims, since baseball caps are hats (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.
