Logical Reasoning - Logical Problems - Discussion

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.

5. 

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.

[A]. I only
[B]. II only
[C]. II and III only
[D]. None of the statements is a known fact.

Answer: Option D

Explanation:

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.

Blah said: (Jan 8, 2014)  
Cap IS NOT EQUAL Baseball Cap? Otherwise I can't find out why I: is not a fact.

Audrey said: (Jan 29, 2014)  
I am considering letter B "Some Baseball caps are blue" Baseball caps are hats, there are black hats and blue hats. Baseball caps are hats. So therefore, some of the baseball caps are blue. "Some" not all. Whew!

Brittany said: (Jul 1, 2014)  
By saying that there are black caps and blue caps wouldn't that mean that some caps are blue?

Nandita said: (Oct 25, 2014)  
If all hats have brims and baseball caps are hats then why 1st conclusion is not considered?

And also if there are black hats and blue hat and baseball caps are hats then why 2nd conclusion is not considered? Please explain.

Spandana said: (Nov 30, 2014)  
If there are black hats and blue hats and a baseball cap is a hat then why can't some caps be blue?

According to me second conclusion can be considered.

Atul said: (Jun 25, 2015)  
My question is as same as @Nandita.

Please explain both option A & B?

Rahul Kumar said: (Sep 6, 2015)  
@Nandita.

Only Baseball caps are hats but all not caps are hats (like Cricket caps).

That is why Fact 1 (All caps have brims) is wrong.

Rahul Kumar said: (Sep 6, 2015)  
@Nandita and all.

Fact 2: There are black hats and blue hats. It is not mixer of black and blue hats. May be all baseball caps are blue, here is also possibilities that all baseball caps are black.

So [B] II only is wrong.

Jacob said: (Jan 3, 2016)  
Based on the tendency of the author to use shortened versions of statements with implicit meanings (or meanings clarified by preceding statements) it is unfair to assume that the author meant to imply that "caps" encompass a group which may contain other forms of caps besides "baseball caps".

There was no reason not to assume that "caps" was simply an abbreviation of "baseball caps" considering the author's prior degree of specificity in terming objects/ideas (E.g. saying "south" to mean directly south---exactly 180 planar degrees from north).

Srujana said: (Feb 4, 2016)  
II is correct because all hats are baseball caps and there are few blue hats and few black hats. So, we can say that some baseball caps are blue.

Teph said: (Jul 27, 2016)  
I had considered Jacob's answer, but went along with the assumption baseball cap = cap.

I guess never assume!

Sadra said: (Sep 30, 2016)  
Statement 1 isn't a fact since there might be caps without brims; Statement 3 to isn't a fact cause baseball caps are hats and all hats have brims; as for Statement 2 is concerned it too isn't a fact because baseball caps are hats and there are black and blue hats but baseball caps might entirely be black, entirely blue or a mixture of blue and black.

So, I thereby conclude that option D is true i.e none of the statement is a fact.

Mastermind said: (Sep 18, 2017)  
The explanation says:.

"Statement II cannot be confirmed, either, since it is possible, given the information, that all baseball caps are black. ".

Ques- Where was it said that all baseball caps are black!?!

Niharika said: (Jul 27, 2018)  
There is no information given that all baseball caps are black.

Then how can you say that all baseball cap is black and 2 is wrong? Explain me.

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