9 votes 9 votes What are the three axioms of functional dependency for the relational databases given by Armstrong. Databases gate1988 normal descriptive databases database-normalization + – go_editor asked Dec 19, 2016 • recategorized Apr 16, 2021 by Lakshman Bhaiya go_editor 1.8k views answer comment Share Follow See 1 comment See all 1 1 comment reply rsansiya111 commented Dec 14, 2022 reply Follow Share The three axioms of functional dependency for the relational databases given by Armstrong are: Reflexivity: This axiom states that every attribute in a set functionally determines itself. This means that if you have a set of attributes A, and you pick any subset of those attributes X, then the values in X will determine the values in X. For example, if you have a relation with the attributes A, B, and C, then the subset {A} will determine the values of A, the subset {B} will determine the values of B, and the subset {C} will determine the values of C. Augmentation: This axiom states that if X functionally determines Y, and Z is a set of attributes that includes Y, then X functionally determines Z. This means that if you have a set of attributes X that determines another set of attributes Y, then X will also determine any set of attributes that includes Y. For example, if you have a relation with the attributes A, B, C, and D, and you know that A functionally determines B, then you can say that A also functionally determines the set {B, C, D}, because it includes B. Transitivity: This axiom states that if X functionally determines Y, and Y functionally determines Z, then X functionally determines Z. This means that if you have a set of attributes X that determines another set of attributes Y, and Y in turn determines another set of attributes Z, then X will also determine Z. For example, if you have a relation with the attributes A, B, C, and D, and you know that A functionally determines B and B functionally determines C, then you can say that A also functionally determines C. 1 votes 1 votes Please log in or register to add a comment.
Best answer 15 votes 15 votes 1. AXIOM OF REFLEXIVITY If $Y\subseteq X$ then $X\rightarrow Y$ 2. AXIOM OF AUGMENTATION If $X\rightarrow Y$ then $XZ\rightarrow YZ$ for any Z 3. AXIOM OF TRANSITIVITY If $X\rightarrow Y$ and $Y\rightarrow Z$ then $X\rightarrow Z$ Aashish S answered Sep 15, 2017 • selected Jul 18, 2019 by Arjun Aashish S comment Share Follow See 1 comment See all 1 1 comment reply Lakshman Bhaiya commented Jan 5, 2020 reply Follow Share If $Y\subseteq X$ then $X\rightarrow Y$ $\implies \text{Axiom of reflexivity is also called a trivial functional dependency.}$ 6 votes 6 votes Please log in or register to add a comment.