The symbol $\rightarrow$ indicates functional dependency in the context of a relational database. Which of the following options is/are TRUE?

We can analyze each option using Armstrong's Axioms and their secondary rules:

• Option (A): False. Having $(X, Y) \rightarrow (Z, W)$ means the combination of $X$ and $Y$ determines $Z$ and $W$. It does not necessarily mean that $X$ alone can determine $(Z, W)$.

• Option (B): True. By the Decomposition Rule (projectivity), if $(X, Y) \rightarrow (Z, W)$, then $(X, Y) \rightarrow Z$ and $(X, Y) \rightarrow W$.

• Option (C): True. By the Pseudotransitivity Rule, if $(X, Y) \rightarrow Z$ and $W \rightarrow Y$, then by augmenting $W \rightarrow Y$ with $X$, we get $(X, W) \rightarrow (X, Y)$. Since $(X, W) \rightarrow (X, Y)$ and $(X, Y) \rightarrow Z$, by transitivity we get $(X, W) \rightarrow Z$.

• Option (D): True. By the Transitivity Rule, if $X \rightarrow Y$ and $Y \rightarrow Z$, then $X \rightarrow Z$.

Hence, options B, C, and D are TRUE.