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EQUIVALENCE OF FUNCTIONAL DEPENDENCIES

You will be given a relation (R) with different functional dependency sets X,Y of that relation , you need to check whether one functional dependency is a subset of other (X⊇Y/ Y"⊇"X ) or both are equal (X=Y).   Consider X and Y are two FD sets for a relation R ,   1)If all FDs of X can be determined from FDs that are present in Y , we can conclude that  Y  ⊇   X    or X ⊆ Y    (Y covers X)  .   2)If all FDs of Y can be determined from FDs that are present in X , we can conclude         X ⊇ Y   or Y ⊆ X (X covers Y) . 3) If   1 and 2 are satisfied   then ,we can say   X=Y  or X and Y are equivale nt .