Let be a relation on , where . State whether R is reflexive, symmetric, transitive or an equivalence relation.
I'm having trouble understand the notation | in the question. I am used to this meaning "such that". The text doesn't explain this problem very well; it says that x must = 9ky were
How do I go about determining the relation here?
The answer given is:
R is reflexive since
R is not symmetric since if x = 2 and y = 18, then but 2 is not divisible by 18.
R is not transitive since if x = 9y and y = 9z then x = 81z, which clearly does no divide 9z. (I don't understand why 81z doesn't divide 9z? is it something to do with the fact that R is is on ?)
Hmmm... is 0|0 true? I think the definition of "divides" is a|b if there is an integer k such that b=ka. Under this definition 0|0 is true since 0=k*0 for ANY integer k. Can someone with a better memory than me remind me if k must be unique.
I wrote the question down word for word in my original post. The next part I mentioned was from the explanation of the solution - not the question itself. I wont be able to reference the exact problem again as the questions are randomly generated in our online text quiz section with unique solution explanations. I could reference another similar question from the same section; it will depend on which question the quiz generates but they are always the same type of question just with slightly different values.