Let $X$ be a smooth, projective variety and $D, E$ two effective divisors of $X$ which correspond to distinct elements on the cohomology group $H^2(X,\mathbb{Q})$. Denote by $H$ a very ample divisor on $X$. Is it then true that $H.D$ and $H.E$ correspond to distinct elements of $H^4(X,\mathbb{Q})$? If not true in general, is there any known condition on $X$ under which this holds true?

Let $X$ be a smooth, projective variety and $D, E$ two effective divisors of $X$ which correspond to distinct elements on the cohomology group $H^2(X,\mathbb{Q})$. Denote by $H$ a very ample divisor on $X$. Is it then true that $H.D$ and $H.E$ correspond to distinct elements of $H^4(X,\mathbb{Q})$? If not true in general, is there any known condition on $X$ under which this holds true?

EDIT: Assume that the underlying field is algebraically closed of characteristic zero and $\dim X \ge 3$.