I've proved the transitivity now, thanks for the help you two. Unfortunately,I've just realized that there's more:
Fill in the blanks:
"The equivalence class containing 5 is given by
[5] = {n\in Z|n has remainder _ when divided by _}"
Am I supposed to put in 0 and 7? If it is, that seems...
Ok, focusing on the symmetric bit for now (sorry about that major typo, HallsofIvy):
x-y=7n
y-x=-7n
m=-7n
I can see that this is leading to some sort of a proof, but I don't really know what to write. Is something like the following enough for proof?:
m and n have a common factor of 7, so x-y...
Please be nice to me, I'm new here. Anyway, help to solve this maths problem would be much appreciated:
Homework Statement
Work out a detailed proof (below) that the relation on the integers defined by p~q if and only if 7|p-q is an equivalence relation:
a) the relation is reflexive
b) the...