Is the relation $5$ divides $(x-y)$ an equivalence relation on $\mathbb Z$?
Can someone helps me out with this question? Thanks in advance!
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2Do you know the properties that must hold for equivalence relations? Can you translate those properties into this context? – kccu Oct 14 '19 at 13:11
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2So, for a relation to be called an equivalence relation, it's customary to have three specific requirements. Have you checked any of them? – Arthur Oct 14 '19 at 13:11
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1You mean the reflexivity, symmetricity and transitivity? – Hanyi Koh Oct 14 '19 at 13:17
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Actually I have done the question and my answer is the relation is equivalence relation on Z.As for reflexivity, I could have(5,5),(6,6)...For symmetricity, I can have (1,6),(6,1)... and for transitivity, I could have(1,6).(6,11),(1,11)....Is my way of proofing this correct? – Hanyi Koh Oct 14 '19 at 13:44
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@HanyiKoh That looks like a very good start. Although you've only proven it for very specific special cases (namely 1, 6 and 11). Your proofs need to cover all possible cases. – Arthur Oct 14 '19 at 14:57