GATE 2015 CS – Question 48

Consider an Entity-Relationship (ER) model in which entity sets $E_1$ and $E_2$ are connected by an $m : n$ relationship $R_{12}$. $E_1$ and $E_3$ are connected by a $1 : n$ (1 on the side of $E_1$ and $n$ on the side of $E_3$) relationship $R_{13}$.

$E_1$ has two single-valued attributes $a_{11}$ and $a_{12}$ of which $a_{11}$ is the key attribute. $E_2$ has two single-valued attributes $a_{21}$ and $a_{22}$ of which $a_{21}$ is the key attribute. $E_3$ has two single-valued attributes $a_{31}$ and $a_{32}$ of which $a_{31}$ is the key attribute. The relationships do not have any attributes.

If a relational model is derived from the above ER model, then the minimum number of relations that would be generated if all the relations are in 3NF is ________.