Equivalence relation means that a relation is reflexive , symmetric , reflexive.
In my problem the relation is not reflexive so is not equivalence.The theme is i have to check out also if it is symmetric (it is) and transitive.
Exercise : x lives 100km from y
Y lives 100km from z.
My question is : does x lives 100km from z ???
(That is only true if x,y,z live in equilateral triangle , but concerning earth is has oceans etc this is not always true.)
Please answer my question
Thanks in advance
In my problem the relation is not reflexive so is not equivalence.The theme is i have to check out also if it is symmetric (it is) and transitive.
Exercise : x lives 100km from y
Y lives 100km from z.
My question is : does x lives 100km from z ???
(That is only true if x,y,z live in equilateral triangle , but concerning earth is has oceans etc this is not always true.)
Please answer my question
Thanks in advance
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I believe that the intended answer is that the relation is not transitive.
As you pointed out, there could be a special case where there are only three people living at the corners of an equilateral triangle. But the sense of the question is that they are asking if this is transitive in general, and that answer is no.
As you pointed out, there could be a special case where there are only three people living at the corners of an equilateral triangle. But the sense of the question is that they are asking if this is transitive in general, and that answer is no.
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It looks like you answered your own question. No! Imagine X===Y===Z.
X and Y are 100km apart, Y and Z are 100km apart, but X and Z are 200km apart.
X and Y are 100km apart, Y and Z are 100km apart, but X and Z are 200km apart.