Which one of the following is true about $R$?

1. In a many-to-one relationship from entity set $E_1$ to entity set $E_2$, each entity in $E_1$ can be associated with at most one entity in $E_2$.

2. Total participation of $E_1$ in $R$ means that every entity in $E_1$ must be associated with at least one entity in $E_2$.

Combining both conditions ("at most one" and "at least one"), every entity in $E_1$ must be associated with exactly one entity in $E_2$. Therefore, option (A) is correct.

Analysis of other options:

• (B) False: A many-to-one mapping forbids any entity in $E_1$ from being linked to multiple entities in $E_2$.

• (C) & (D) False: Since $|E_1| > |E_2|$ and all entities of $E_1$ participate, by the Pigeonhole Principle, at least one entity in $E_2$ must be linked to more than one entity in $E_1$.