Let $$R\left( {A,B,C,D} \right)$$ be a relational schema with the following functional dependencies:
$$A \to B,\,\,B \to C,\,\,C \to D$$ and $$D \to B.$$
The decomposition of $$R$$ into $$(A,B), (B,C)$$ and $$(B,D)$$

Consider the following relational schemes for a library database. Book ( Title, Author, Catalog_ no, Publisher, Year, Pr ice ) Collection ( Title, Author, Catalog no )
With in the following functional dependencies:
$${\rm I}.\,\,\,\,\,\,$$ Title Author $$ \to $$ Catalog_no
$${\rm II}.\,\,\,\,$$ Catalog_no $$ \to $$ Title Author Publisher Year
$${\rm III}.\,\,\,\,$$ Publisher Title Year $$ \to $$ Price

Assume { Author, Title } is the key for both schemes. Which of the following statements is true?

Which one of the following statements if FALSE?

The following functional dependencies are given :
$$\eqalign{ & AB \to CD,\,AF \to D,\,\,DE \to F, \cr & C \to G.\,\,\,\,\,\,\,\,\,\,F \to E.\,\,\,\,\,\,\,\,\,G \to A. \cr} $$

Which one of the following options is false?