If a∈G, then the “left" and “right" equivalence classes containing a are given by [a]∼L={g∈G∣a∼Lg} and [a]∼R={g∈G∣a∼Rg}. The next theorem t...If a∈G, then the “left" and “right" equivalence classes containing a are given by [a]∼L={g∈G∣a∼Lg} and [a]∼R={g∈G∣a∼Rg}. The next theorem tells us that the equivalence classes determined by ∼L and ∼R are indeed the left and right cosets of H≤G, respectively.