I'm doing this problem in the book - their are 2 of this kind and they have no answers in the back.. so i thought ill post one. Let S be the Cartesian coodinate plane R x R and define a relation R on S by (a,b)R(c,d) iff a+d=b+c. Verify that R is an equivalence relation and describe the equivalence class E(7,3) ....So i want to show that the 3 properties of an equivalence reltion holds: (reflective propery, symmetric propery and transitive propery.) 1. reflective propery (a,b)=(a,b) and (c,d)=(c,d)......(not hard) 2. symmetric propery Let (a,b) be in A and (c,d) be in B and if A R B, then (a,b) = (c,d) so, (c,d) = (a,b) and thus, B R A. How does that sound? 3. transitive propery i have no idea how to start this i mean, the property states "if xRy and yRz, then xRz" so will this work:? if (a,b)=(c,d) and (c,d)=(e,f), then (a,b)=(e,f) but then i feel like i making things up when i put in (e,f)?