GATE CS 2018 Q11 — ER-model

To determine the correct statement, let us analyze the properties of the relationship $R$ from $E_1$ to $E_2$ step-by-step:

1. Many-to-One Relationship from $E_1$ to $E_2$: This constraint means that each entity in $E_1$ can be associated with at most one entity in $E_2$.
2. Total Participation of $E_1$ in $R$: This constraint means that every entity in $E_1$ must participate in the relationship $R$. That is, each entity in $E_1$ is associated with at least one entity in $E_2$.

Combining these two constraints for $E_1$:

$$\text{At least one} \quad \cap \quad \text{At most one} \quad = \quad \text{Exactly one}$$

Thus, every entity in $E_1$ is associated with exactly one entity in $E_2$. This makes Option A correct.

Why other options are incorrect:

• Option B: Incorrect, because the many-to-one constraint from $E_1$ to $E_2$ prevents any entity in $E_1$ from being associated with more than one entity in $E_2$.
• Options C and D: Since $|E_1| > |E_2|$ and every entity in $E_1$ maps to exactly one entity in $E_2$, by the Pigeonhole Principle, at least one entity in $E_2$ must be associated with multiple entities in $E_1$. This invalidates both "exactly one" (Option C) and "at most one" (Option D) for $E_2$.