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I was reading some logical test here. I reported it down below

Given the following premises, state whether the conclusions are true, false, or unknown:

All athletes are coaches, but not all coaches are athletes. All coaches live in Chicago. No students are athletes, but all students are coaches. Some teachers are both athletes and students. Some parents are teachers, but no parents are students or athletes.

  1. All parents live in Chicago.

A) True

B) False

C) Uncertain

  1. All coaches are students.

A) True

B) False

C) Uncertain

however if "No students are athletes", I don't understand how "some teachers are both athletes and students".

user26857
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roi_saumon
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  • The premises, as you observed, are inconsistent. Maybe the intention of the text is now to conclude that everything is true using the principle of explosion (ex falso sequitur quodlibet). – Magdiragdag Nov 03 '21 at 12:52
  • I agree with your puzzlement... In addition, to say that "some teachers are student" sounds very strange. – Mauro ALLEGRANZA Nov 03 '21 at 12:56
  • @Magdiragdag. actually they say that 4)->uncertain and 5)->false. I think the test is just wrong... – roi_saumon Nov 03 '21 at 12:57
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    The depicted Venn diagram "depicts" a different premise: "Some teachers are either athletes or students". – Mauro ALLEGRANZA Nov 03 '21 at 13:01
  • @MauroALLEGRANZA, yes I agree with you – roi_saumon Nov 03 '21 at 13:02
  • @MauroALLEGRANZA The Venn diagram also seems to suggest all teachers are coaches, but this is not obvious to me and may not matter. What does matter for 5 to be false is that there is at least one non-student coach, which would be satisfied by there being at least one athlete, and that depends on words. "Some teachers are athletes and some teachers are students" would work, suggesting the original used both in a non-standard way – Henry Nov 03 '21 at 13:47
  • It could be that the statement is intended to mean the following: "Some teachers are athletes and some teachers are students." – PiGuy314 Nov 05 '21 at 17:34

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