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?
Thanks.
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.
On this webpage is the following quote:
"Clearly, and . By convention, for every except 0 (Hardy and Wright 1979, p. 1)"
Let us see. Conventions are conventions. If we define in iff for some then, is reflexive (no problem). If we exclude then is not reflexive by convention (no problem). That depends on the context: in the context of Measure Theory (by convention), in the context of infinite products (by convention) etc. For those reasons and looking at all the previous answers I suggested to terrorsquid to transcribe the exact formulation of the problem, taking (besides) into account that he,or the problem (who knows?) says for some .
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.