GATE CS 2005 Q75 — ER-model

To find the minimum number of tables required to represent the given E/R diagram in the relational model, we analyze each component step-by-step:

1. Entities $E_1$ and $E_2$: Each entity with simple-valued attributes generally requires its own table to store its attributes.
   • Let the table for $E_1$ have primary key $K_1$.
   • Let the table for $E_2$ have primary key $K_2$.
2. One-to-Many Relationship $R_1$: In a $1:N$ (one-to-many) relationship, we do not need a separate table. Instead, we can merge the relationship into the table of the entity on the "many" ($N$) side by adding the primary key of the "one" side entity as a foreign key.
   • For example, if the relationship is $1:N$ from $E_1$ to $E_2$, we can represent $R_1$ by adding $K_1$ as a foreign key in the table for $E_2$.
   • Thus, $E_1$, $E_2$, and $R_1$ can be represented using just 2 tables:
     • $\text{Table } E_1(K_1, \dots)$
     • $\text{Table } E_2(K_2, \dots, K_1)$
3. Many-to-Many Relationship $R_2$: An $M:N$ (many-to-many) relationship cannot be merged into either of the entity tables without causing redundancy or violating normalization rules. Therefore, it always requires a separate table containing the primary keys of both participating entities as foreign keys.
   • $\text{Table } R_2(K_1, K_2)$

Combining these, the minimum number of tables required is:

Hence, the minimum number of tables required is 3.