Please be nice to me, I'm new here. Anyway, help to solve this maths problem would be much appreciated: 1. The problem statement, all variables and given/known data 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 relation is symmetric c) the relation is transitive 2. Relevant equations p~q if and only if 7|p-q 3. The attempt at a solution a) (I'm pretty sure this is done right) If relation is reflexive then: x[tex]\in[/tex]S[tex]\rightarrow[/tex] (x,x) [tex]\in[/tex]R Therefore x~x 7|x-x since x-x=0 and 7|0 Therefore relation is reflexive. That's the easy bit. Now: b)If relation is symmetric then: x~y [tex]\leftrightarrow[/tex] y~x And I don't know how to go on from there. Please help me!!