GATE CS 1987 Q2n — Normal Forms

A functional dependency $X \rightarrow Y$ holds on a relation $r$ if and only if for any two tuples $t_1, t_2 \in r$, whenever $t_1[X] = t_2[X]$, it must also be that $t_1[Y] = t_2[Y]$.

For the given tuples $t_1 = \langle 1, 2 \rangle$ and $t_2 = \langle 2, 2 \rangle$:

• $t_1[X] = 1$ and $t_2[X] = 2$.
• Since $t_1[X] \neq t_2[X]$, the condition for the functional dependency is vacuously satisfied.

Therefore, both tuples can coexist in $r$ simultaneously without violating $X \rightarrow Y$. The statement is TRUE (represented by 1).