I'm stuck with this equivelance relations question,
'Let ~be the relation on the set Z of all integers defined by m~n provided that 10m+ n is divisible by 11.
1. Prove that ~ is an equivalence relation.'
First for reflexitivity, we do m~m and thus 10m+m=11m which surely is divisible by 11.
Now for it being symmetric, we do n~m which means 10n+m and we need to prove that that is divisible by 11, however do not not how to prove this.
Finaly for transitivity, I do not know how to approach it here - its kinda got me confused.
Help would be very much appreciated, thank you very much.