Which of the following is an empty set?

Doing set theory in maths and stuck.. I guessed b and c but not sure...





a. The set of men with no teeth


b. The set of months of the year with 32 days


c. The set of straight lines drawn on the surface of a sphere


d. The set of prime numbers between 35 and 43

Which of the following is an empty set?
The answer is 'b'. You can draw straight lines on the surface of a sphere. They are called tangents (with only one point touching the surface)
Reply:a) Unfortunately, there are men with no teeth, sad but true. We should do our best to avoid this in the name of human solidarity, but the fact is that , for now, this is not an empty set.





b) No month of the year has 32 days, so we have the empty set.





c) In the scope of Euclidean geometry, no line drawn on the surface of a sphere is a straight line. So, we have the empty set ( I suppose you mean the entire line lies on the sphere's surface)





d) Clearly this is not the empty set, because 37 and 41 are prime and lie between 35 and 43.
Reply:I'm in favor of both (b) and (c). In a section on set theory, I doubt they're trying to throw you a curve ball on non-Euclidean geometry. I think we can safely assume that straight means straight in the Euclidean sense, and that "on the sphere" means that the entire line lies completely on the sphere.





I would only argue the semantics of "straight line" in a class where geometry is the focus.
Reply:The answer is b. Months either have 30 or 31 days. February being the special case in which it has 28 days or 29 days if


it is a leap year.
Reply:It's definitely B.





As for C, one can draw a tangential line on the surface of the sphere.
Reply:b


why dont you look at the answer
Reply:B is the odd one out as all the other choices are at least mildly logical
Reply:Set b is the answer. A straight line can be "bent" but still remain straight in a 2 dimensional form, ie lines of latitude and longitude on the earth. If we were to presume that c was an empty set then we would be denying the existence of non-Euclidean geometry and therefore the existence of the D-circle.
Reply:b - I did set theory with the OU and am 98% sure.


But it was some years ago!


It might be c but, intuatively, b!
Reply:How many Months have 32 days. So the set is empty
Reply:There are no months with 32 days.


As for c, it depends on your definition of a straight line. In some contexts a great circle can be considered a straight line.

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