I'm a bit confused about how to prove that R is reflexive.
By definition, R, a relation in a set S, is reflexive if and only if ∀x∈S, xRx.
Since (a, α)R(b, β), we know that aβ = bα.
Then to prove that this is reflexive, based on the definition, we would have to show that ((a, α)R(b, β)) R ((a, α)R(b, β). After this, I'm not sure as to how to prove why this is reflexive.
Could we possibly do something like (aβ = bα) R (aβ = bα) is reflexive? Or does ((a, α)R(b, β)) R ((a, α)R(b, β)) already show that it is reflexive itself?