Theorem 1.1. Let S1 = {0, −an−1n}, S2 = {z : zn + azn−1 + b = 0} where n(≥ 7)be an integer and a and b be two nonzero constants such that zn+azn−1+b = 0 hasno multiple root. If f and g be two non-constant meromorphic functions having nosimple pole such that Ef (S1, 0) = Eg(S1, 0) and Ef (S2, 2) = Eg(S2, 2), then f ≡ g.Theorem 1.2. Let Si, i = 1, 2 and f and g be taken as in Theorem 1.1 wheren(≥ 8) is an integer. If Ef (S1, 0) = Eg(S1, 0) and Ef (S2, 1) = Eg(S2, 1), thenf ≡ g.Next by calculation it can be shown that in Lemma-2.2 we would always have p = 0.So in Lemma-2.2 we should replace N(r, 0; f |≥ p+1)+Nr, −an−1n; f |≥ p + 1byN(r, 0; f) + Nr, −an−1n; f. In that case the statement of the Lemma-2.2. shouldbe replaced byLemma-2.2. Let S1 and S2 be defined as in Theorem 1.1 and F, G be givenby (2.1). If for two non-constant meromorphic functions f and g, Ef (S1, 0) =Eg(S1, 0), Ef (S2, 0) = Eg(S2, 0), where H 6≡ 0 thenN(r, H) ≤ N(r, 0; f) + Nr, −an − 1n; f+ N∗(r, 1; F, G)+N(r, ∞; f) + N(r, ∞; g) + N0(r, 0; f0) + N0(r, 0; g0),where N0(r, 0; f0) is the reduced counting function of those zeros of f0which arenot the zeros of ff − an−1n(F − 1) and N0(r, 0; g0) is similarly define