Table of contents 
Introduction 
1 Crore+ students have signed up on EduRev. Have you? 
Given a Relation with different FD sets for that relation, we have to find out whether one FD set is subset of other or both are equal.
How to find relationship between two FD sets?Let FD1 and FD2 are two FD sets for a relation R.
All these three cases can be shown using Venn diagram as:
Q. Let us take an example to show the relationship between two FD sets. A relation R(A, B, C, D) having two FD sets FD1 = {A > B, B > C, AB > D} and FD2 = {A > B, B > C, A > C, A > D}
Step 1: Checking whether all FDs of FD1 are present in FD2
As all FDs in set FD1 also hold in set FD2, FD2 ⊃ FD1 is true.
Step 2: Checking whether all FDs of FD2 are present in FD1
As all FDs in set FD2 also hold in set FD1, FD1 ⊃ FD2 is true.
Step 3: As FD2 ⊃ FD1 and FD1 ⊃ FD2 both are true FD2 = FD1 is true. These two FD sets are semantically equivalent.
Q. Let us take another example to show the relationship between two FD sets. A relation R2(A, B, C, D) having two FD sets FD1 = {A > B, B > C,A > C} and FD2 = {A > B, B > C, A > D}
Step 1: Checking whether all FDs of FD1 are present in FD2
As all FDs in set FD1 also hold in set FD2, FD2 ⊃ FD1 is true.
Step 2: Checking whether all FDs of FD2 are present in FD1
As all FDs in set FD2 do not hold in set FD1, FD2 ⊄ FD1.
Step 3: In this case, FD2 ⊃ FD1 and FD2 ⊄ FD1, these two FD sets are not semantically equivalent.
The term Armstrong axioms refer to the sound and complete set of inference rules or axioms, introduced by William W. Armstrong, that is used to test the logical implication of functional dependencies. If F is a set of functional dependencies then the closure of F, denoted as F^+, is the set of all functional dependencies logically implied by F. Armstrong’s Axioms are a set of rules, that when applied repeatedly, generates a closure of functional dependencies.
AxiomsThese rules can be derived from the above axioms.
Why armstrong axioms refer to the Sound and Complete?
By sound, we mean that given a set of functional dependencies F specified on a relation schema R, any dependency that we can infer from F by using the primry rules of amrmstrong axioms holds in every relation state r of R that satisfies the dependencies in F.
By complete, we mean that using primary rules of amrstrong axioms repeatedly to infer dependencies until no more dependencies can be inferred results in the complete set of all possible dependencies that can be inferred from F.
1 videos49 docs15 tests

Use Code STAYHOME200 and get INR 200 additional OFF

Use Coupon Code 
1 videos49 docs15 tests
